The connection matrix theory for Morse decompositions

Keywords

Morse code, Connection (principal bundle), Mathematics, Morse homology, Morse theory

References

• Isolated Invariant Sets and the Morse IndexCharles C. Conley — 1978
• Classification of Traveling Wave Solutions of Reaction-Diffusion Systems.Konstantin Mischaikow — 1985
• Index filtrations and the homology index braid for partially ordered Morse decompositionsRobert Franzosa — 1986
• The Morse index of an isolated invariant set is a connected simple systemHenry L. Kurland — 1981
• Homotopy invariants of repeller-attractor pairs, II. Continuation of R-A pairsHenry L. Kurland — 1983
• Shock Waves and Reaction-Diffusion EquationsJoel Smoller — 1983
• The Connection Matrix Theory for Semiflows on (Not Necessarily Locally Compact) Metric SpacesRobert Franzosa, Konstantin Mischaikow — 1988
• CONNECTED SIMPLE SYSTEMS AND THE CONLEY INDEX OF ISOLATED INVARIANT SETSDietmar Salamon — 1985
• The continuation theory for Morse decompositions and connection matricesRobert Franzosa — 1988
• Homotopy invariants of repeller-attractor pairs. I. The Püppe sequence of an R-A pairHenry L. Kurland — 1982
• Morse‐type index theory for flows and periodic solutions for Hamiltonian EquationsCharles C. Conley, Eduard Zehnder — 1984
• Mappings and homological properties in the Conley index theoryChristopher McCord, K Mccord, C Conley — 1988
• Connecting orbits in one-parameter families of flowsJames F. Reineck, C Conley, C Conley — 1988
• Index Filtrations and the Homology Index Braid for Partially Ordered Morse DecompositionsRobert Franzosa — 1986
• The Continuation Theory for Morse Decompositions and Connection MatricesRobert Franzosa — 1988
• Connected Simple Systems and the Conley Index of Isolated Invariant Sets.D. Salamon — 1984

Cited by

• On the suspension isomorphism for index braids in a singular perturbation problemMaria C. Carbinatto, Krzysztof P. Rybakowski — 2008
• The Conley index for fast–slow systems II: Multidimensional slow variable☆Tomáš Gedeon, Hiroshi Kokubu, Konstantin Mischaikow — 2006
• Dynamical systems and shapesJ. J. Sánchez-Gabites — 2008
• Conley-Morse Chain MapsTodd Keith Moeller — 2005
• A restricted Conley index and robust dynamics of coupled oscillator systemsA. Ismail — 2013
• THE CONLEY INDEX ON THE MORSE THEORYYoung-Sun Jung, Kwang-Pak Park — 1993
• On foundations of the Conley index theoryRoman Srzednicki — 1999
• Connection matrix theory for discrete dynamical systemsPiotr Bartłomiejczyk, Zdzisław Dzedzej — 1999
• Connection matrix pairsDavid Richeson — 1999
• Index filtrations and Morse decompositions for discrete dynamical systemsPiotr Bartłomiejczyk, Zdzisław Dzedzej — 1999
• Directional transition matrixHiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka — 1999
• Connection matrices and transition matricesChristopher McCord, James F. Reineck — 1999
• Matrizes de conexão via o complexo de Morse-WittenDahisy V. S. Lima, K. Rezende — 2010
• Algebraic transition matrices in the Conley index theoryRobert Franzosa, Konstantin Mischaikow — 1998
• The Conley index theory: A brief introductionKonstantin Mischaikow — 1999
• Generalized topological transition matrixRobert Franzosa, Ketty A. de Rezende, Ewerton R. Vieira — 2013
• Equivalence of graded module braids and interlocking sequencesZin Arai — 2003
• The Conley index for decompositions of isolated invariant setsAndrzej Szymczak — 1995
• The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractorMichael Grinfeld, Amy Novick-Cohen — 1999
• On the global dynamics of attractors for scalar delay equationsChristopher McCord, Konstantin Mischaikow — 1996

Related papers

• Some remarks on Morse theory for posets, homological Morse theory and finite manifoldsElías Gabriel Minian — 2010
• Morse complexes for shape segmentation and homological analysis: discrete models and algorithmsLeila De Floriani, Ulderico Fugacci, Federico Iuricich — 2015
• Discrete Morse theory for weighted simplicial complexesChengyuan Wu, Shiquan Ren, Jie Wu — 2019
• Computing homology and persistent homology using iterated Morse decompositionPaweł Dłotko, Hubert Wagner — 2012
• Lectures on Morse HomologyAugustin Banyaga, David Hurtubise — 2005
• A complex in Morse theory computing intersection homologyUrsula Ludwig — 2017
• A combinatorial method to compute explicit homology cycles using Discrete Morse TheoryDmitry N. Kozlov — 2019
• Morse–Conley–Floer homologyThomas O. Rot, Robert Vandervorst — 2013