Warwick Tucker

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All published works

Action	Title	Year	Authors
+ PDF Chat	Efficient and Validated Numerical Evaluation of Abelian Integrals	2023	Florent Bréhard Nicolas Brisebarre Mioara Joldeş Warwick Tucker
+ PDF Chat	Nowhere coexpanding functions	2023	Andrew Cook Andy Hammerlindl Warwick Tucker
+ PDF Chat	Lower bounds on the Hausdorff dimension of some Julia sets	2023	Artem Dudko Igors Gorbovickis Warwick Tucker
+	Nowhere coexpanding functions	2023	Andrew Cook Andy Hammerlindl Warwick Tucker
+ PDF Chat	Computer assisted proofs in dynamical systems	2022	Maciej J. Capiński J. D. Mireles James Warwick Tucker Daniel Wilczak Jan Bouwe van den Berg
+	Lower bounds on the Hausdorff dimension of some Julia sets	2022	Artem Dudko Igors Gorbovickis Warwick Tucker
+	The number of relative equilibria in the PCR4PB	2022	Jordi-Lluís Figueras Warwick Tucker Piotr Zgliczyński
+	The Songling system has exactly four limit cycles	2021	Zbigniew Galias Warwick Tucker
+	Scalable Multivariate Histograms	2020	Raazesh Sainudiin Warwick Tucker Tilo Wiklund
+	A New Lower Bound on the Hilbert Number for Quartic Systems	2019	Florent Bréhard Nicolas Brisebarre Mioara Joldeş Warwick Tucker
+	Enclosing all zeros of a system of analytic functions	2018	Joel Dahné M. F. Ciappina Warwick Tucker
+	Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor	2018	Zbigniew Galias Warwick Tucker
+	Invertibility Properties of Singular Integral Operators Associated with the Lamé and Stokes Systems on Infinite Sectors in Two Dimensions	2017	Irina Mitrea Katharine Ott Warwick Tucker
+	Fixed points of a destabilized Kuramoto–Sivashinsky equation	2015	Ferenc A. Bartha Warwick Tucker
+	A database of rigorous and high-precision periodic orbits of the Lorenz model	2015	Roberto Barrio Ángeles Dena Warwick Tucker
+	Is the Hénon attractor chaotic?	2015	Zbigniew Galias Warwick Tucker
+	On the structure of existence regions for sinks of the Hénon map	2014	Zbigniew Galias Warwick Tucker
+	A systematic approach to find periodic sinks of the Henon map close to the classical case	2014	Zbigniew Galias Warwick Tucker
+	NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP	2013	Zbigniew Galias Warwick Tucker
+	Combination of exhaustive search and continuation method for the study of sinks in the H&#x00E9;non map	2013	Zbigniew Galias Warwick Tucker
+	Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals	2013	Jordi-Lluís Figueras Warwick Tucker Jordi Villadelprat
+	Mapped Regular Pavings	2012	Jennifer Harlow Raazesh Sainudiin Warwick Tucker
+	Chapter Four. Automatic Differentiation	2011	Warwick Tucker
+ PDF Chat	A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity	2011	Oswald Fogelklou Warwick Tucker Gunilla Kreiss
+ PDF Chat	On a computer-aided approach to the computation of Abelian integrals	2011	Tomas Johnson Warwick Tucker
+	VALIDATED STUDY OF THE EXISTENCE OF SHORT CYCLES FOR CHAOTIC SYSTEMS USING SYMBOLIC DYNAMICS AND INTERVAL TOOLS	2011	Zbigniew Galias Warwick Tucker
+ PDF Chat	A Note on the Convergence of Parametrised Non-Resonant Invariant Manifolds	2011	Tomas Johnson Warwick Tucker
+ PDF Chat	AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7	2010	Tomas Johnson Warwick Tucker
+	AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION	2010	Tomas Johnson Warwick Tucker
+	Rigorous parameter estimation for noisy mixed-effects models	2010	Alexander S. Danis Andrew C. Hooker Warwick Tucker
+	A rigorous lower bound for the stability regions of the quadratic map	2009	Warwick Tucker Daniel Wilczak
+	Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems	2009	Zbigniew Galias Warwick Tucker
+	Fundamentals of Chaos	2009	Warwick Tucker
+	A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five	2009	Tomas Johnson Warwick Tucker
+ PDF Chat	Automated computation of robust normal forms of planar analytic vector fields	2009	Tomas Johnson Warwick Tucker
+	Parametrisation of local invariant manifolds	2008	Tomas Johnson Warwick Tucker
+	Rigorous parameter reconstruction for differential equations with noisy data	2008	Tomas Johnson Warwick Tucker
+ PDF Chat	Rigorous study of short periodic orbits for the Lorenz system	2008	Zbigniew Galias Warwick Tucker
+ PDF Chat	How to measure a degree of mismatch between probability models, p-boxes, etc.: A decision-theory-motivated utility-based approach	2008	Luc Longpré Scott Ferson Warwick Tucker
+ PDF Chat	Short periodic orbits for the Lorenz system	2008	Zbigniew Galias Warwick Tucker
+	Robust normal forms for saddles of analytic vector fields	2004	Warwick Tucker
+ PDF Chat	Some counterexamples for the spectral-radius conjecture	2003	Irina Mitrea Warwick Tucker
+	Computing accurate Poincaré maps	2002	Warwick Tucker
+	The Lorenz Attractor Exists – An Auto-Validated Proof	2002	Warwick Tucker
+ PDF Chat	A Rigorous ODE Solver and Smale’s 14th Problem	2002	Warwick Tucker
+	Computational algorithms for ordinary differential equations	2000	Warwick Tucker
+	Residually reducible representations and modular forms . Sur les espaces fonctionnels dont la source est le classifiant d'un groupe de Lie compact commutatif . Non-uniformly expanding dynamics in maps with singularities and criticalities . Mean dimension, small entropy factors and an embedding theorem	2000	Christopher Skinner Andrew Wiles François-Xavier Dehon Jean Lannes Stephano Luzzatto Warwick Tucker Elon Lindenstrauss
+ PDF Chat	Non-uniformly expanding dynamics in maps with singularities and criticalities	1999	Stefano Luzzatto Warwick Tucker
+	The Lorenz attractor exists	1999	Warwick Tucker
+	Rigorous models for the Lorenz equations	1996	Warwick Tucker

Common Coauthors

Coauthor	Papers Together
Zbigniew Galias	11
Tomas Johnson	8
Daniel Wilczak	2
Igors Gorbovickis	2
Andy Hammerlindl	2
Nicolas Brisebarre	2
Raazesh Sainudiin	2
Irina Mitrea	2
Florent Bréhard	2
Artem Dudko	2
Mioara Joldeş	2
Andrew Cook	2
Gunilla Kreiss	1
Stefano Luzzatto	1
Joel Dahné	1
Piotr Zgliczyński	1
Roberto Barrio	1
Elon Lindenstrauss	1
Oswald Fogelklou	1
Luc Longpré	1
J. D. Mireles James	1
Jennifer Harlow	1
Jordi Villadelprat	1
Andrew Wiles	1
M. F. Ciappina	1
Jan Bouwe van den Berg	1
Maciej J. Capiński	1
Jean Lannes	1
François-Xavier Dehon	1
Tilo Wiklund	1
Ferenc A. Bartha	1
Stephano Luzzatto	1
Christopher Skinner	1
Ángeles Dena	1
Katharine Ott	1
Scott Ferson	1
Jordi-Lluís Figueras	1
Andrew C. Hooker	1
Jordi-Lluís Figueras	1
Alexander S. Danis	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	A Rigorous ODE Solver and Smale’s 14th Problem	2002	Warwick Tucker	12
+ PDF Chat	Deterministic Nonperiodic Flow	1963	Edward N. Lorenz	10
+	Chaos in the Lorenz equations: a computer-assisted proof	1995	Konstantin Mischaikow Marian Mrożek	9
+	The Lorenz attractor exists	1999	Warwick Tucker	8
+	COUNTING LOW-PERIOD CYCLES FOR FLOWS	2006	Zbigniew Galias	7
+	The Dynamics of the Henon Map	1991	Michael Benedicks Lennart Carleson	7
+	Computer assisted proof of chaos in the Lorenz equations	1998	Zbigniew Galias Piotr Zgliczyński	7
+ PDF Chat	Structural stability of Lorenz attractors	1979	John Guckenheimer R. F. Williams	7
+ PDF Chat	Centennial History of Hilbert's 16th Problem	2002	Yu. Ilyashenko	7
+ PDF Chat	Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem	1998	Robert Roussarie	6
+	Mathematical problems for the next century	1998	Steve Smale	6
+	A unified proof on the weak Hilbert 16th problem for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>	2005	Fengde Chen Chengzhi Li Jaume Llibre Zenghua Zhang	5
+ PDF Chat	On a computer-aided approach to the computation of Abelian integrals	2011	Tomas Johnson Warwick Tucker	5
+	Finiteness theorems for limit cycles	1990	Yu. Ilyashenko	5
+ PDF Chat	A two-dimensional mapping with a strange attractor	1976	M. Hénon	5
+ PDF Chat	The structure of Lorenz attractors	1979	R. F. Williams	5
+	INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS	2001	Zbigniew Galias	5
+	Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem	1998	Robert Roussarie	4
+	Limit Cycles of Differential Equations	2024	Colin Christopher Chengzhi Li Joan Torregrosa	4
+	EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS	1978	Genrich Belitskii	4
+ PDF Chat	The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms	1979	Sheldon E. Newhouse	4
+	Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac	1992	Jean Écalle	4
+ PDF Chat	A shooting approach to the Lorenz equations	1992	S. P. Hastings William C. Troy	4
+	Complex Interval Arithmetic and Its Applications	1998	Miodrag S. Petković Ljiljana D. Petković	3
+	Homoclinic bifurcation to a transitive attractor of Lorenz type	1989	Clark Robinson	3
+	Ordinary Differential Equations	2002	Philip Hartman	3
+	A Strange, Strange Attractor	1976	John Guckenheimer	3
+	Finiteness Theorems for Limit Cycles	1991	Yu. Ilyashenko	3
+ PDF Chat	Phase Portraits of Planar Vector Fields: Computer Proofs	1995	John Guckenheimer	3
+ PDF Chat	Rigorous Numerics for Partial Differential Equations: The Kuramoto—Sivashinsky Equation	2001	Piotr Zgliczyński Konstantin Mischaikow	3
+	The topological classification of Lorenz attractors	1978	D.A.J. Rand	3
+ PDF Chat	CAPD::DynSys: A flexible C++ toolbox for rigorous numerical analysis of dynamical systems	2020	Tomasz Kapela Marian Mrożek Daniel Wilczak Piotr Zgliczyński	3
+	Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians	1998	Emil Horozov Iliya D. Iliev	3
+	Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations	1980	Eugene L. Allgower Kurt Georg	3
+ PDF Chat	Symbolic dynamics and periodic orbits of the Lorenz attractor*	2003	Divakar Viswanath	3
+ PDF Chat	Lorenz attractors through Šil'nikov-type bifurcation. Part I	1990	Marek Rychlik	3
+ PDF Chat	Rigorous study of short periodic orbits for the Lorenz system	2008	Zbigniew Galias Warwick Tucker	3
+	Perturbation from an elliptic Hamiltonian of degree four—IV figure eight-loop	2003	Freddy Dumortier Chengzhi Li	3
+ PDF Chat	Almost Every Real Quadratic Map Is Either Regular or Stochastic	2002	Mikhail Lyubich	3
+	Validated solutions of initial value problems for ordinary differential equations	1999	Nedialko S. Nedialkov Kenneth R. Jackson George F. Corliss	3
+	Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields	1983	John Guckenheimer Philip Holmes	3
+	NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP	2013	Zbigniew Galias Warwick Tucker	3
+ PDF Chat	Absolutely continuous invariant measures for one-parameter families of one-dimensional maps	1981	Michael Jakobson	3
+	On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation	2007	Hongxian Zhou Wei Xu Shuang Li Ying Zhang	3
+	A cubic system with thirteen limit cycles	2009	Chengzhi Li Changjian Liu Jiazhong Yang	3
+	Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation	1987	Andreas Griewank Andrea Walther	3
+	Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations	2000	Vladimir Kozlov Vladimir Maz’ya J. Roßmann	2
+	Perturbations from an Elliptic Hamiltonian of Degree Four	2001	Freddy Dumortier Chengzhi Li	2
+ PDF Chat	Bifurcation to infinitely many sinks	1983	Clark Robinson	2
+	Ordinary differential equations in the complex domain	1976	Einar Hille	2