Brian R. Hunt

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All published works

Action	Title	Year	Authors
+ PDF Chat	Exploring the Potential of Hybrid Machine-Learning/Physics-Based Modeling for Atmospheric/Oceanic Prediction Beyond the Medium Range	2024	Dhruvit Patel Troy Arcomano Brian R. Hunt Istvan Szunyogh Edward Ott
+	Stabilizing Machine Learning Prediction of Dynamics: Noise and Noise-inspired Regularization	2022	Alexander Wikner Brian R. Hunt Joseph E. Harvey Michelle Girvan Edward Ott
+ PDF Chat	Using data assimilation to train a hybrid forecast system that combines machine-learning and knowledge-based components	2021	Alexander Wikner Jaideep Pathak Brian R. Hunt Istvan Szunyogh Michelle Girvan Edward Ott
+ PDF Chat	Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems	2020	Alexander Wikner Jaideep Pathak Brian R. Hunt Michelle Girvan Troy Arcomano Istvan Szunyogh Andrew Pomerance Edward Ott
+ PDF Chat	Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics	2020	Pantelis R. Vlachas Jay Pathak Brian R. Hunt Themistoklis P. Sapsis Michelle Girvan Edward Ott Petros Koumoutsakos
+ PDF Chat	Separation of chaotic signals by reservoir computing	2020	Sanjukta Krishnagopal Michelle Girvan Edward Ott Brian R. Hunt
+	Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics	2019	Pantelis R. Vlachas Jaideep Pathak Brian R. Hunt Themistoklis P. Sapsis Michelle Girvan Edward Ott Petros Koumoutsakos
+	The Recurrent Processing Unit: Hardware for High Speed Machine Learning	2019	Heidi Komkov Alessandro Restelli Brian R. Hunt Liam Shaughnessy Itamar Shani Daniel P. Lathrop
+	Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics	2019	Pantelis R. Vlachas Jaideep Pathak Brian R. Hunt Themistoklis P. Sapsis Michelle Girvan Edward Ott Petros Koumoutsakos
+ PDF Chat	Attractor reconstruction by machine learning	2018	Zhixin Lu Brian R. Hunt Edward Ott
+	Attractor Reconstruction by Machine Learning through Generalized Synchronization	2018	Zhixin Lu Brian R. Hunt Edward Ott
+ PDF Chat	Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model	2018	Jaideep Pathak Alexander Wikner Rebeckah K. Fussell Sarthak Chandra Brian R. Hunt Michelle Girvan Edward Ott
+	Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data	2017	Jaideep Pathak Zhixin Lu Brian R. Hunt Michelle Girvan Edward Ott
+ PDF Chat	Defining chaos	2015	Brian R. Hunt Edward Ott
+	Defining Chaos	2015	Brian R. Hunt Edward Ott
+	Absolute Continuity of a Function and Uniform Integrability of Its Divided Differences	2015	Patrick Fitzpatrick Brian R. Hunt
+	Defining Chaos	2015	Brian R. Hunt Edward Ott
+	Atmospheric Dynamics for Efficient Ensemble Kalman Filtering	2014	Edward Ott Brian R. Hunt Istvan Szunyogh M. Corazza Eugenia Kalnay James A. Yorke
+ PDF Chat	Coupled skinny baker's maps and the Kaplan–Yorke conjecture	2013	Maik Gröger Brian R. Hunt
+	Differential equations with MATLAB : updated for MATLAB 2011b (7.13), Simulink 7.8, and Symbolic math toolbox 5.7	2012	Brian R. Hunt
+ PDF Chat	Comment on “Long time evolution of phase oscillator systems” [Chaos <b>19</b>, 023117 (2009)]	2011	Edward Ott Brian R. Hunt Thomas M. Antonsen
+	Ensemble regional data assimilation using joint states	2011	Y. Yoon Brian R. Hunt Edward Ott Istvan Szunyogh
+ PDF Chat	Approximating invariant densities of metastable systems	2010	Cecilia González‐Tokman Brian R. Hunt Paul E. Wright
+	Prevalence	2010	Brian R. Hunt Vadim Yu. Kaloshin
+	Scaling laws for bubbling bifurcations	2009	Cecilia González‐Tokman Brian R. Hunt
+ PDF Chat	Synchronization in networks of networks: The onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators	2008	Ernest Barreto Brian R. Hunt Edward Ott Paul So
+ PDF Chat	Weighted Percolation on Directed Networks	2008	Juan G. Restrepo Edward Ott Brian R. Hunt
+ PDF Chat	Approximating the largest eigenvalue of network adjacency matrices	2007	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Estimating the State of Large Spatiotemporally Chaotic Systems	2007	Matthew Cornick Brian R. Hunt Edward Ott Michael F. Schatz
+	Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems	2007	Anton Gorodetski Brian R. Hunt V. A. Kaloshin
+ PDF Chat	Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter	2007	Brian R. Hunt Eric J. Kostelich Istvan Szunyogh
+ PDF Chat	Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I	2007	V. A. Kaloshin Brian R. Hunt
+	Estimating the State of Large Spatiotemporally Chaotic Systems	2007	Matthew Cornick Brian R. Hunt Edward Ott Michael F. Schatz
+ PDF Chat	Characterizing the Dynamical Importance of Network Nodes and Links	2006	Juan G. Restrepo Edward Ott Brian R. Hunt
+ PDF Chat	Emergence of Coherence in Complex Networks of Heterogeneous Dynamical Systems	2006	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Practice Set A: Algebra and Arithmetic	2006	Brian R. Hunt Ronald L. Lipsman Jonathan Rosenberg Kevin R. Coombes John E. Osborn Garrett Stuck
+	MATLAB Programming	2006	Brian R. Hunt Ronald L. Lipsman Jonathan Rosenberg Kevin R. Coombes John E. Osborn Garrett Stuck
+	Practice Set B: Calculus, Graphics, and Linear Algebra	2006	Brian R. Hunt Ronald L. Lipsman Jonathan Rosenberg Kevin R. Coombes John E. Osborn Garrett Stuck
+ PDF Chat	The effect of projections on fractal sets and measures in Banach spaces	2006	William Ott Brian R. Hunt V. A. Kaloshin
+ PDF Chat	Scale Dependence of Branching in Arterial and Bronchial Trees	2006	Juan G. Restrepo Edward Ott Brian R. Hunt
+ PDF Chat	Synchronization in large directed networks of coupled phase oscillators	2006	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems	2006	Anton Gorodetski Brian R. Hunt V. A. Kaloshin
+ PDF Chat	Formation of multifractal population patterns from reproductive growth and local resettlement	2005	Jonathan Ozik Brian R. Hunt Edward Ott
+ PDF Chat	Onset of synchronization in large networks of coupled oscillators	2005	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Efficient Data Assimilation for Spatiotemporal Chaos: a Local Ensemble Transform Kalman Filter	2005	Brian R. Hunt Eric J. Kostelich Istvan Szunyogh
+	Differential equations with MATLAB : updated for MATLAB 7 and Simulink 6	2005	Brian R. Hunt
+ PDF Chat	Desynchronization Waves and Localized Instabilities in Oscillator Arrays	2004	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Critical saddle-node bifurcations and Morse–Smale maps	2004	Brian R. Hunt Todd Young
+ PDF Chat	Estimating the state of large spatio-temporally chaotic systems	2004	Edward Ott Brian R. Hunt Istvan Szunyogh Aleksey V. Zimin Eric J. Kostelich M. Corazza Eugenia Kalnay D. J. Patil James A. Yorke
+ PDF Chat	Spatial patterns of desynchronization bursts in networks	2004	Juan G. Restrepo Edward Ott Brian R. Hunt
+	Power-law decay and self-similar distributions in stadium-type billiards	2004	Douglas Armstead Brian R. Hunt Edward Ott
+	Two Models for the Study of Congested Internet Connections	2004	Ian Frommer Eric Harder Brian R. Hunt Ryan Lance Edward Ott James A. Yorke
+ PDF Chat	A local ensemble Kalman filter for atmospheric data assimilation	2004	Edward Ott Brian R. Hunt Istvan Szunyogh Aleksey V. Zimin Eric J. Kostelich M. Corazza Eugenia Kalnay D. J. Patil James A. Yorke
+	Introduction	2004	Brian R. Hunt Tien-Yien Li Judy Kennedy Helena E. Nusse
+ PDF Chat	Fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions	2003	Jongwon Kim Sang-Yoon Kim Brian R. Hunt Edward Ott
+ PDF Chat	Anomalous diffusion in infinite horizon billiards	2003	Douglas Armstead Brian R. Hunt Edward Ott
+	Bifurcation scenarios for bubbling transition	2003	Aleksey V. Zimin Brian R. Hunt Edward Ott
+ PDF Chat	Long Time Algebraic Relaxation in Chaotic Billiards	2002	Douglas Armstead Brian R. Hunt Edward Ott
+ PDF Chat	Evolving networks with multispecies nodes and spread in the number of initial links	2002	Jongwon Kim Brian R. Hunt Edward Ott
+	SLYRB measures: natural invariant measures for chaotic systems	2002	Brian R. Hunt Judy Kennedy Tien-Yien Li Helena E. Nusse
+	Exploiting Local Low Dimensionality of the Atmospheric Dynamics for Efficient Ensemble Kalman Filtering	2002	Edward Ott Brian R. Hunt Istvan Szunyogh M. Corazza Eugenia Kalnay D. J. Patil James A. Yorke Aleksey V. Zimin Eric J. Kostelich
+	Final Report for List 1, Project 1	2002	Brian R. Hunt
+	SLYRB measures: natural invariant measures for chaotic systems	2002	Brian R. Hunt Judy Kennedy Tien-Yien Li Helena E. Nusse
+	A Local Ensemble Kalman Filter for Atmospheric Data Assimilation	2002	Edward Ott Brian R. Hunt Istvan Szunyogh Aleksey V. Zimin Eric J. Kostelich M. Corazza Eugenia Kalnay D. J. Patil James A. Yorke
+	Fractal Properties of Robust Strange Nonchaotic Attractors	2001	Brian R. Hunt Edward Ott
+ PDF Chat	Local Low Dimensionality of Atmospheric Dynamics	2001	D. J. Patil Brian R. Hunt Eugenia Kalnay James A. Yorke Edward Ott
+	A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II	2001	V. A. Kaloshin Brian R. Hunt
+	A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I	2001	V. A. Kaloshin Brian R. Hunt
+	Optimal periodic orbits of continuous time chaotic systems	2000	Tsung‐Hsun Yang Brian R. Hunt Edward Ott
+	A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms	2000	Vadim Yu. Kaloshin Brian R. Hunt
+	Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces	1999	Brian R. Hunt Vadim Yu. Kaloshin
+	Box-counting dimension without boxes: Computing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>from average expansion rates	1999	Paul So Ernest Barreto Brian R. Hunt
+	Sporadically Fractal Basin Boundaries of Chaotic Systems	1999	Brian R. Hunt Edward Ott Epaminondas Rosa
+	Optimal orbits of hyperbolic systems	1999	Guo‐Cheng Yuan Brian R. Hunt
+	Calculating topological entropy for transient chaos with an application to communicating with chaos	1998	Joeri Jacobs Edward Ott Brian R. Hunt
+	The Mathematica ® Primer	1998	Kevin R. Coombes Brian R. Hunt Ronald L. Lipsman John E. Osborn Garrett Stuck
+	Differential Equations with Mathematica, Revised for Mathematica 3.0	1998	Kevin R. Coombes Ronald L. Lipsman Brian R. Hunt John E. Osborn Garrett Stuck
+ PDF Chat	The Hausdorff dimension of graphs of Weierstrass functions	1998	Brian R. Hunt
+	Differential equations with Maple	1998	Kevin R. Coombes Garrett Stuck Ronald L. Lipsman John E. Osborn Brian R. Hunt
+	Bifurcation Diagrams	1998	Helena E. Nusse James A. Yorke Brian R. Hunt Eric J. Kostelich
+	Scaling of the durations of chaotic transients in windows of attracting periodicity	1997	Joeri Jacobs Edward Ott Brian R. Hunt
+	Structure in the parameter dependence of order and chaos for the quadratic map	1997	Brian R. Hunt Edward Ott
+	How projections affect the dimension spectrum of fractal measures	1997	Brian R. Hunt Vadim Yu. Kaloshin
+	From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space	1997	Ernest Barreto Brian R. Hunt Celso Grebogi James A. Yorke
+	Control of Chaos by Means of Embedded Unstable Periodic Orbits	1997	Edward Ott Brian R. Hunt
+ PDF Chat	Correlation dimension for iterated function systems	1997	Wai Chin Brian R. Hunt James A. Yorke
+	Fractal dimensions of chaotic saddles of dynamical systems	1996	Brian R. Hunt Edward Ott James A. Yorke
+ PDF Chat	Fractal properties of critical invariant curves	1996	Brian R. Hunt Konstantin Khanin Yakov G. Sinai James A. Yorke
+	Intermingled basins for the triangle map	1996	J. C. Alexander Brian R. Hunt Ittai Kan James A. Yorke
+ PDF Chat	Estimating invariant measures and Lyapunov exponents	1996	Brian R. Hunt
+	Optimal periodic orbits of chaotic systems occur at low period	1996	Brian R. Hunt Edward Ott
+	Maximum local Lyapunov dimension bounds the box dimension of chaotic attractors	1996	Brian R. Hunt
+	Optimal Periodic Orbits of Chaotic Systems	1996	Brian R. Hunt Edward Ott
+ PDF Chat	The Prevalence of Continuous Nowhere Differentiable Functions	1994	Brian R. Hunt
+ PDF Chat	The prevalence of continuous nowhere differentiable functions	1994	Brian R. Hunt
+	Differential equations with mathematica	1993	Brian R. Hunt Ronald L. Lipsman John E. Osborn Donald A. Outing Jonathan Rosenberg
+ PDF Chat	When Cantor Sets Intersect Thickly	1993	Brian R. Hunt Ittai Kan James A. Yorke
+	Prevalence: an addendum	1993	Brian R. Hunt Timothy Sauer James A. Yorke
+ PDF Chat	When Cantor sets intersect thickly	1993	Brian R. Hunt Ittai Kan James A. Yorke
+ PDF Chat	Prevalence. An addendum to: “Prevalence: a translation-invariant ‘almost every’ on infinite-dimensional spaces” [Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 217–238; MR1161274 (93k:28018)]	1993	Brian R. Hunt Timothy Sauer James A. Yorke
+	Prevalence: an addendum	1993	Brian R. Hunt Timothy Sauer James A. Yorke
+	Prevalence: a translation-invariant ``almost every'' on infinite-dimensional spaces	1992	Brian R. Hunt
+ PDF Chat	Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces	1992	Brian R. Hunt Timothy Sauer James A. Yorke
+	Prevalence: a translation-invariant ``almost every'' on infinite-dimensional spaces	1992	Brian R. Hunt
+ PDF Chat	Smooth Dynamics on Weierstrass Nowhere Differentiable Curves	1991	Brian R. Hunt James A. Yorke
+ PDF Chat	Smooth dynamics on Weierstrass nowhere differentiable curves	1991	Brian R. Hunt James A. Yorke
+	When all solutions of x′ = −∑ qi(t) x(t − Ti(t)) oscillate	1984	Brian R. Hunt James A. Yorke
+	Performance of familial mentally deficient children in response to motivation on the Goodenough draw-aman test.	1957	Brian R. Hunt Patterson Rm

Common Coauthors

Coauthor	Papers Together
Edward Ott	53
James A. Yorke	22
Istvan Szunyogh	11
Michelle Girvan	9
Juan G. Restrepo	9
Ronald L. Lipsman	7
Eric J. Kostelich	7
John E. Osborn	7
Garrett Stuck	6
Kevin R. Coombes	6
V. A. Kaloshin	6
Jaideep Pathak	6
Eugenia Kalnay	6
M. Corazza	5
D. J. Patil	5
Aleksey V. Zimin	5
Jonathan Rosenberg	4
Vadim Yu. Kaloshin	4
Alexander Wikner	4
Timothy Sauer	4
Helena E. Nusse	4
Pantelis R. Vlachas	3
Ittai Kan	3
Judy Kennedy	3
Douglas Armstead	3
Petros Koumoutsakos	3
Ernest Barreto	3
Zhixin Lu	3
Themistoklis P. Sapsis	3
Anton Gorodetski	2
Tien-Yien Li	2
Cecilia González‐Tokman	2
Joeri Jacobs	2
Paul So	2
Jongwon Kim	2
Troy Arcomano	2
Paul E. Wright	1
Tien-Yien Li	1
Wai Chin	1
Todd Young	1
Sanjukta Krishnagopal	1
Eric Harder	1
Itamar Shani	1
Michael F. Schatz	1
Liam Shaughnessy	1
Patterson Rm	1
Michael F. Schatz	1
Celso Grebogi	1
Epaminondas Rosa	1
Tsung‐Hsun Yang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces	1992	Brian R. Hunt Timothy Sauer James A. Yorke	14
+	The dimension of chaotic attractors	1983	J. Doyne Farmer Edward Ott James A. Yorke	11
+ PDF Chat	Prevalence. An addendum to: “Prevalence: a translation-invariant ‘almost every’ on infinite-dimensional spaces” [Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 217–238; MR1161274 (93k:28018)]	1993	Brian R. Hunt Timothy Sauer James A. Yorke	8
+ PDF Chat	Dimension, entropy and Lyapunov exponents	1982	Lai-Sang Young	8
+	Ergodic theory of chaos and strange attractors	1985	Jean-Pierre Eckmann David Ruelle	7
+	Chaotic behavior of multidimensional difference equations	1979	James L. Kaplan James A. Yorke	7
+	Embedology	1991	Timothy Sauer James A. Yorke Martin Casdagli	7
+ PDF Chat	Deterministic Nonperiodic Flow	1963	Edward N. Lorenz	7
+ PDF Chat	Statistical mechanics of complex networks	2002	Réka Albert Albert‐László Barabási	7
+ PDF Chat	Spectra of random graphs with given expected degrees	2003	Fan Chung Linyuan Lü Van Vu	6
+	Chaos in Dynamical Systems	1992	Daniel Zwillinger	6
+	Detecting strange attractors in turbulence	1981	Floris Takens	6
+ PDF Chat	Absolutely continuous invariant measures for one-parameter families of one-dimensional maps	1981	Michael Jakobson	6
+ PDF Chat	The Lyapunov dimension of a nowhere differentiable attracting torus	1984	James L. Kaplan John Mallet‐Paret James A. Yorke	6
+	The infinite number of generalized dimensions of fractals and strange attractors	1983	H. G. E. Hentschel Itamar Procaccia	6
+ PDF Chat	Emergence of Scaling in Random Networks	1999	Albert‐László Barabási Réka Albert	6
+	Crises, sudden changes in chaotic attractors, and transient chaos	1983	Celso Grebogi Edward Ott James A. Yorke	5
+ PDF Chat	Local Low Dimensionality of Atmospheric Dynamics	2001	D. J. Patil Brian R. Hunt Eugenia Kalnay James A. Yorke Edward Ott	5
+ PDF Chat	The Structure and Function of Complex Networks	2003	Michael Newman	5
+ PDF Chat	Fractal Geometry: Mathematical Foundations and Applications.	1990	K. J. Falconer	5
+	Are the dimensions of a set and its image equal under typical smooth functions?	1997	Timothy Sauer James A. Yorke	5
+ PDF Chat	Fat baker's transformations	1984	J. C. Alexander James A. Yorke	5
+	GIBBS MEASURES IN ERGODIC THEORY	1972	Yakov G. Sinai	5
+	Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions	1954	J. M. Marstrand	5
+ PDF Chat	On the existence of invariant measures for piecewise monotonic transformations	1973	A. Lasota James A. Yorke	5
+	Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data	2017	Jaideep Pathak Zhixin Lu Brian R. Hunt Michelle Girvan Edward Ott	5
+ PDF Chat	The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms	1979	Sheldon E. Newhouse	5
+	Generic Hyperbolicity in the Logistic Family	1997	Jacek Graczyk Grzegorz Świątek	4
+ PDF Chat	Some relations between dimension and Lyapounov exponents	1981	F. Ledrappier	4
+	Scaling behavior of chaotic systems with riddled basins	1993	Edward Ott John C. Sommerer J. C. Alexander Ittai Kan James A. Yorke	4
+ PDF Chat	Ergodic transformations from an interval into itself	1978	Tien-Yien Li James A. Yorke	4
+	Hausdorff dimension, orthogonal projections and intersections with planes	1975	Pertti Mattila	4
+	On Hausdorff dimension of projections	1968	Robert Kaufman	4
+	Fractal basin boundaries	1985	Steven W. McDonald Celso Grebogi Edward Ott James A. Yorke	4
+	Optimal Periodic Orbits of Chaotic Systems	1996	Brian R. Hunt Edward Ott	4
+ PDF Chat	Frequency synchronization in a random oscillator network	2004	Takashi Ichinomiya	4
+	The ergodic theory of AxiomA flows	1975	Rufus Bowen David Ruelle	4
+ PDF Chat	Dimension formula for random transformations	1988	F. Ledrappier Lai-Sang Young	4
+	The Dynamics of the Henon Map	1991	Michael Benedicks Lennart Carleson	4
+	How projections affect the dimension spectrum of fractal measures	1997	Brian R. Hunt Vadim Yu. Kaloshin	4
+	The liapunov dimension of strange attractors	1983	Paul O. Frederickson James L. Kaplan Ellen Yorke James A. Yorke	4
+ PDF Chat	Onset of synchronization in large networks of coupled oscillators	2005	Juan G. Restrepo Edward Ott Brian R. Hunt	4
+	Diffeomorphisms with infinitely many sinks	1974	Sheldon E. Newhouse	4
+ PDF Chat	A two-dimensional mapping with a strange attractor	1976	M. Hénon	4
+	Applications conservant une mesure absolument continue par rapport àdx sur [0, 1]	1977	David Ruelle	4
+	Topology of Generic Multijet Preimages and Blow-Up via Newton Interpolation	1998	Alexei Grigoriev Sergeî Yakovenko	4
+ PDF Chat	Smooth dynamics on Weierstrass nowhere differentiable curves	1991	Brian R. Hunt James A. Yorke	4
+	Introduction to the modern theory of dynamical systems	1996	Anatole Katok Boris Hasselblatt	4
+ PDF Chat	Synchronization in large directed networks of coupled phase oscillators	2006	Juan G. Restrepo Edward Ott Brian R. Hunt	4
+	Integral Geometry and Geometric Probability	2004	Luis A. Santaló Mark Kac	4