Hiroshi Kokubu

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All published works

Action	Title	Year	Authors
+ PDF Chat	Global Dynamics of Ordinary Differential Equations: Wall Labelings, Conley Complexes, and Ramp Systems	2024	Marcio Gameiro Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka Bernardo Rivas Ewerton R. Vieira Daniel Gameiro
+	Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities	2021	W.J. Duncan Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities	2021	W.J. Duncan Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	Topological Computation Analysis of Meteorological Time-Series Data	2019	Hidetoshi Morita Masaru Inatsu Hiroshi Kokubu
+ PDF Chat	Explicit transversality conditions and local bifurcation diagrams for Bogdanov–Takens bifurcation on center manifolds	2018	Yang Li Hiroshi Kokubu Kazuyuki Aihara
+	Topological computation analysis of meteorological time-series data	2018	Hidetoshi Morita Masaru Inatsu Hiroshi Kokubu
+ PDF Chat	Global dynamics for steep nonlinearities in two dimensions	2016	Tomáš Gedeon Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+ PDF Chat	Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity	2016	Ippei Obayashi Shinya Aoi Kazuo Tsuchiya Hiroshi Kokubu
+ PDF Chat	A study of rigorous ODE integrators for multi-scale set-oriented computations	2016	Tomoyuki Miyaji Paweł Pilarczyk Marcio Gameiro Hiroshi Kokubu Konstantin Mischaikow
+ PDF Chat	Inducing a map on homology from a correspondence	2015	Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Paweł Pilarczyk
+	Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions	2015	Tomáš Gedeon Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	Inducing a map on homology from a correspondence	2014	Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Paweł Pilarczyk
+	Formation Mechanism of a Basin of Attraction for Passive Dynamic Walking Induced by Intrinsic Hyperbolicity	2014	Ippei Obayashi Shinya Aoi Kazuo Tsuchiya Hiroshi Kokubu
+	Inducing a map on homology from a correspondence	2014	Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Paweł Pilarczyk
+	Capturing the Global Behavior of Dynamical Systems with Conley-Morse Graphs	2013	Zin Arai Hiroshi Kokubu Ippei Obayashi
+	About the unfolding of a Hopf-zero singularity	2013	Freddy Dumortier Santiago González-Varas Ibáñez Hiroshi Kokubu Carles Simö
+ PDF Chat	A topological computation approach to the interior crisis bifurcation	2012	Hiroshi Kokubu Hiroe Oka
+	Combinatorial-topological framework for the analysis of global dynamics	2012	Justin Bush Marcio Gameiro Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Ippei Obayashi Paweł Pilarczyk
+	A Combinatorial Framework for Analysis of Global Dynamics and Bifurcations	2012	Hiroshi Kokubu Konstantin Mischaikow
+ PDF Chat	Recent development in rigorous computational methods in dynamical systems	2009	Zin Arai Hiroshi Kokubu Paweł Pilarczyk
+ PDF Chat	Quantitative hyperbolicity estimates in one-dimensional dynamics	2008	Sarah Day Hiroshi Kokubu Stefano Luzzatto Konstantin Mischaikow Hiroe Oka Paweł Pilarczyk
+	Rigorous verification of cocoon bifurcations in the Michelson system	2007	Hiroshi Kokubu Daniel Wilczak Piotr Zgliczyński
+	The Conley index for fast–slow systems II: Multidimensional slow variable	2005	Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	Cocoon bifurcation in three-dimensional reversible vector fields	2005	Freddy Dumortier Santiago González-Varas Ibáñez Hiroshi Kokubu
+	On transition matrices	2005	Hiroshi Kokubu
+	Existence of a Singularly Degenerate Heteroclinic Cycle in the Lorenz System and Its Dynamical Consequences: Part I	2004	Hiroshi Kokubu Robert Roussarie
+	None	2002	Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	Homoclinic-Doubling Cascades	2001	Ale Jan Homburg Hiroshi Kokubu Vincent Naudot
+	New aspects in the unfolding of the nilpotent singularity of codimension three	2001	Freddy Dumortier Santiago Ibnez Hiroshi Kokubu
+	Chaotic dynamics in ${\mathbb Z}_2$-equivariant unfoldings of codimension three singularities of vector fields in ${\mathbb R}^3$	2000	Freddy Dumortier Hiroshi Kokubu
+	The existence of infinitely many homoclinic doubling bifurcations from some codimension 3 homoclinic orbits	1997	Hiroshi Kokubu Vincent Naudot
+	Linear Grading Function and Further Reduction of Normal Forms	1996	Hiroshi Kokubu Hiroe Oka Duo Wang
+	Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation	1996	Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka
+	MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS	1996	Hiroshi Kokubu Motomasa Komuro Hiroe Oka
+	Successive homoclinic doublings bifurcations from oribt-flip	1996	Motomasa Komuro Hiroshi Kokubu Hiroe Oka
+	The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit	1994	Ale Jan Homburg Hiroshi Kokubu Martin Krupa
+	Bifurcations toN-homoclinic orbits andN-periodic orbits in vector fields	1993	Masashi Kisaka Hiroshi Kokubu Hiroe Oka
+	Bifurcations of Continuous Piecewise-Linear Vector Fields	1993	Takashi Matsumoto Motomasa Komuro Hiroshi Kokubu Ryuji Tokunaga
+	Fundamental Concepts in Bifurcations	1993	Takashi Matsumoto Motomasa Komuro Hiroshi Kokubu Ryuji Tokunaga
+	Normal forms for nonlinear vector fields. II. Applications	1989	Leon O. Chua Hiroshi Kokubu
+	Homoclinic and heteroclinic bifurcations of Vector fields	1988	Hiroshi Kokubu
+	Normal forms for nonlinear vector fields. I. Theory and algorithm	1988	Leon O. Chua Hiroshi Kokubu
+	On A Bifurcation of Heteroclinic Orbits(Dynamical Systems and Applications)	1987	Hiroshi Kokubu
+ PDF Chat	On a codimension $2$ bifurcation of heteroclinic orbits	1987	Hiroshi Kokubu
+	Constrained Lorenz-like attractors	1985	Hiroe Oka Hiroshi Kokubu
+	Normal forms for parametrized vector fields and its application to bifurcations of some reaction diffusion equations	1984	Hiroshi Kokubu

Common Coauthors

Coauthor	Papers Together
Hiroe Oka	15
Konstantin Mischaikow	15
Tomáš Gedeon	7
Paweł Pilarczyk	7
Shaun Harker	6
Motomasa Komuro	4
Freddy Dumortier	4
Ippei Obayashi	4
Marcio Gameiro	3
Masaru Inatsu	2
Ale Jan Homburg	2
Ryuji Tokunaga	2
Takashi Matsumoto	2
Shinya Aoi	2
Zin Arai	2
W.J. Duncan	2
Hidetoshi Morita	2
Santiago González-Varas Ibáñez	2
Leon O. Chua	2
Vincent Naudot	2
Kazuo Tsuchiya	2
Daniel Gameiro	1
Daniel Wilczak	1
Sarah Day	1
Martin Krupa	1
Kazuyuki Aihara	1
Stefano Luzzatto	1
Justin Bush	1
Masashi Kisaka	1
Robert Roussarie	1
Carles Simó	1
Tomoyuki Miyaji	1
Duo Wang	1
Piotr Zgliczyński	1
Yang Li	1
Santiago Ibnez	1
Bernardo Rivas	1
Ewerton R. Vieira	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Isolated Invariant Sets and the Morse Index	1978	Charles C. Conley	11
+	Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields	1983	John Guckenheimer Philip Holmes	8
+ PDF Chat	An Algorithmic Approach to Chain Recurrence	2005	William D. Kalies Konstantin Mischaikow Robert Vandervorst	7
+	Branching of double pulse solutions from single pulse solutions in nerve axon equations	1987	Eiji Yanagida	7
+ PDF Chat	Singularities of vector fields	1974	Floris Takens	6
+ PDF Chat	Lorenz attractors through Šil'nikov-type bifurcation. Part I	1990	Marek Rychlik	6
+	Normal forms for singularities of vector fields	1984	Shigehiro Ushiki	5
+	Uniqueness of connecting orbits in the equation Y(3) = Y2 − 1	1986	Christopher McCord	5
+	Homoclinic bifurcation at resonant eigenvalues	1990	S.N. Chow Bo Deng Bernold Fiedler	5
+	Graph Approach to the Computation of the Homology of Continuous Maps	2005	Konstantin Mischaikow Marian Mrożek Paweł Pilarczyk	5
+ PDF Chat	Deterministic Nonperiodic Flow	1963	Edward N. Lorenz	5
+	Combinatorial-topological framework for the analysis of global dynamics	2012	Justin Bush Marcio Gameiro Shaun Harker Hiroshi Kokubu Konstantin Mischaikow Ippei Obayashi Paweł Pilarczyk	5
+ PDF Chat	Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps	2013	Shaun Harker Konstantin Mischaikow Marian Mrożek Vidit Nanda	4
+	New aspects in the unfolding of the nilpotent singularity of codimension three	2001	Freddy Dumortier Santiago Ibnez Hiroshi Kokubu	4
+	Methods of Bifurcation Theory	1982	Shui-Nee Chow Jack K. Hale	4
+	Conley Index	2002	Konstantin Mischaikow Marian Mrożek	4
+	The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit	1994	Ale Jan Homburg Hiroshi Kokubu Martin Krupa	4
+ PDF Chat	Germs of Diffeomorphisms in the Plane	1981	Freddy Dumortier Paulo R. Rodrigues Robert Roussarie	4
+	Bifurcations toN-homoclinic orbits andN-periodic orbits in vector fields	1993	Masashi Kisaka Hiroshi Kokubu Hiroe Oka	4
+	Local and global behavior near homoclinic orbits	1984	Paul Glendinning Colin Sparrow	4
+	ON THE GENERATION OF A PERIODIC MOTION FROM TRAJECTORIES DOUBLY ASYMPTOTIC TO AN EQUILIBRIUM STATE OF SADDLE TYPE	1968	L P Šil'nikov	3
+	Homoclinic twisting bifurcations and cusp horseshoe maps	1993	Bo Deng	3
+	Cocoon bifurcation in three-dimensional reversible vector fields	2005	Freddy Dumortier Santiago González-Varas Ibáñez Hiroshi Kokubu	3
+	Strange attractor in the unfolding of an inclination-flip homoclinic orbit	1996	Vincent Naudot	3
+ PDF Chat	A Computational Approach to Conley’s Decomposition Theorem	2006	Hyun-Ju Ban William D. Kalies	3
+ PDF Chat	A study of rigorous ODE integrators for multi-scale set-oriented computations	2016	Tomoyuki Miyaji Paweł Pilarczyk Marcio Gameiro Hiroshi Kokubu Konstantin Mischaikow	3
+	Crises, sudden changes in chaotic attractors, and transient chaos	1983	Celso Grebogi Edward Ott James A. Yorke	3
+	The Sil'nikov problem, exponential expansion, strong λ-lemma, C1-linearization, and homoclinic bifurcation	1989	Bo Deng	3
+	Quantitative universality for a class of nonlinear transformations	1978	Mitchell J. Feigenbaum	3
+	C1 Lohner Algorithm	2002	Piotr Zgliczyński	3
+ PDF Chat	Applications of Centre Manifold Theory.	1979	Jack Carr	3
+	Functional equations and conjugacy of local diffeomorphisms of a finite smoothness class	1974	Genrich Belitskii	3
+ PDF Chat	A two-dimensional mapping with a strange attractor	1976	M. Hénon	3
+	Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria	2002	Ale Jan Homburg	3
+ PDF Chat	Connected simple systems, transition matrices, and heteroclinic bifurcations	1992	Christopher McCord Konstantin Mischaikow	3
+	Homoclinic bifurcation to a transitive attractor of Lorenz type	1989	Clark Robinson	3
+ PDF Chat	Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3	1987	Freddy Dumortier Robert Roussarie Jorge Sotomayor	3
+	Exponential expansion with Šil'nikov's saddle-focus	1989	Bo Deng	3
+ PDF Chat	Dichotomies in Stability Theory	1978	W. A. Coppel	2
+ PDF Chat	A Numerical Method for Constructing the Hyperbolic Structure of Complex Henon Mappings	2006	Suzanne Lynch Hruska	2
+	Using Melnikov's method to solve Silnikov's problems	1990	Xiao-Biao Lin	2
+	Shil'nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on R3	2003	Santiago González-Varas Ibáñez Jesús Rodríguez	2
+	On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies	2007	Zin Arai	2
+	T-points: A codimension two heteroclinic bifurcation	1986	Paul Glendinning Colin Sparrow	2
+	A characterization of the minimum cycle mean in a digraph	1978	Richard M. Karp	2
+ PDF Chat	A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems	2004	Sarah Day Oliver Junge Konstantin Mischaikow	2
+ PDF Chat	Structural stability of Lorenz attractors	1979	John Guckenheimer R. F. Williams	2
+	Generic Observability of Differentiable Systems	1981	Dirk Aeyels	2
+ PDF Chat	Symmetric Heteroclinic Connections in the Michelson System: A Computer Assisted Proof	2005	Daniel Wilczak	2
+	The Conley Index on Compact Anr’s Is of Finite Type	1990	Marian Mrożek	2