Displaying similar documents to “A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms.”

Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere

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...

Retracts, fixed point index and differential equations.

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.