Dynamical systems and shapes

Keywords

Algebraic topology, Homotopy, Topology (electrical circuits), Dynamical systems theory, Attractor

References

• Isolated Invariant Sets and the Morse IndexCharles C. Conley — 1978
• Shapes of compacta and ANR-systemsSibe Mardešić, Jack Segal — 1971
• Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinairesTadeusz Ważewski — 1948
• Theory Of RetractsKarol Borsuk — 1967
• Topological problems of the theory of dynamical systemsViktor Vladimirovich Nemytskii — 1954
• Theory of dynamical systemsЯ.Г. Синай — 1970
• The structure of orbits in dynamical systemsJ. Aarts — 1988
• Equivalence of the Borsuk and the ANR-system approach to shapesSibe Mardešić, Jack Segal — 1971
• The Homotopy Index and Partial Differential EquationsKrzysztof P. Rybakowski — 1987
• WITTEN'S COMPLEX AND INFINITE DIMENSIONAL MORSE THEORYAndreas Floer — 1989
• Stability theory of dynamical systemsN. P. Bhatia, George Philip Szegö — 1970
• Shape Theory: The Inverse System ApproachS. Mardešić — 1982
• Shape Theory: An IntroductionJerzy Dydak, Jack Segal — 1978
• Normally Hyperbolic Invariant Manifolds in Dynamical SystemsStephen Wiggins — 1994
• Concerning homotopy properties of compactaKarol Borsuk — 1968
• Morse equations and unstable manifolds of isolated invariant setsJosé Manuel Rodríguez Sanjurjo — 2003
• Morse theory, the Conley index and Floer homologyDietmar Salamon — 1990
• Isolating blocks for Morse flowsMaria Alice Bertolim, Ketty A. de Rezende, Oziride Manzoli Neto — 2007
• On the global structure of invariant regions of flows with asymptotically stable attractorsAntonio Giraldo, José Manuel Rodríguez Sanjurjo — 1999
• Smoothing continuous flows on two-manifolds and recurrencesCarlos Gutiérrez — 1986

Cited by

• Regions of attraction, limits and end points of an exterior discrete semi-flowJ.M. García-Calcines, L. J. Hernández, M. Marañón — 2014
• Singular Continuations of AttractorsAntonio Giraldo, José Manuel Rodríguez Sanjurjo — 2009
• An approach to the shape Conley index without index pairsJ. J. Sánchez-Gabites — 2011
• Intrinsic shape of the chain recurrent setNikita Shekutkovski, Martin Shoptrajanov — 2016
• Characterization of Topologically Transitive Attractors for Analytic Plane FlowsMartin Shoptrajanov, Nikita Shekutkovski — 2015
• Regular blocks and Conley index of isolated invariant continua in surfacesHéctor Barge — 2016
• Flows in R^2_+R+2 without interior fixed points, global attractors and bifurcationsHéctor Barge, José Manuel Rodríguez Sanjurjo — 2018
• Omega limits, prolongational limits and almost periodic points of a continuous flow via exterior spacesDepartamento de Matemáticas, Estadística e I.O., Universidad de La Laguna, 38200 La Laguna, Spain, J.M. García-Calcines, Luis Javier Hernández Paricio — 2017
• Dissipative flows, global attractors and shape theoryHéctor Barge, José Manuel Rodríguez Sanjurjo — 2018
• A Conley index study of the evolution of the Lorenz strange setHéctor Barge, José Manuel Rodríguez Sanjurjo — 2018
• Topología y dinámica de conjuntos non-saddle e índice de Conley en variedadesHéctor Barge Yáñez — 2017
• On a Lie algebraic structure associated with a non-linear dynamical systemJosé Ramón Guzmán — 2019
• Limit and end functors of dynamical systems via exterior spacesJ.M. García-Calcines, L.Hernandez Paricio, María Teresa Rivas Rodríguez — 2012
• Čech cohomology, homoclinic trajectories and robustness of non-saddle setsHéctor Barge — 2020
• Shape-invariant Neighborhoods of Nonsaddle SetsMartin Shoptrajanov, Nikita Shekutkovski — 2020
• Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systemsHéctor Barge, José Manuel Rodríguez Sanjurjo — 2021
• Cech cohomology, homoclinic trajectories and robustness of non-saddle setHéctor Barge — 2021
• Shape of compacta as extension of weak homotopy of finite spacesPedro J. Chocano, Manuel A. Morón, Francisco R. Ruiz del Portal — 2021
• A combinatorial description of shape theoryPedro J. Chocano, Manuel A. Morón, Francisco R. Ruiz del Portal — 2022
• Flows in R 2 + without interior fixed points, global attractors and bifurcationsH. Barge, J. Sanjurjo — 2017

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