Discretization and Morse-Smale dynamical systems on planar discs.
Garay, B.M. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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Garay, B.M. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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Andrzej Bielecki (2000)
Annales Polonici Mathematici
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This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system...
Richeson, David, Wiseman, Jim (2004)
International Journal of Mathematics and Mathematical Sciences
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Rafael Ortega (2008)
RACSAM
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Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
Richeson, David, Wiseman, Jim (2003)
The New York Journal of Mathematics [electronic only]
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Fedorenko, V.V., Smítal, J. (1991)
Acta Mathematica Universitatis Comenianae. New Series
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François Béguin, Sylvain Crovisier, Frédéric Le Roux (2007)
Annales scientifiques de l'École Normale Supérieure
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Pujals, Enrique R., Sambarino, Martín (2000)
Annals of Mathematics. Second Series
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J. Aarts (1988)
Fundamenta Mathematicae
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Giesl, P. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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