Un teorema bien conocido en dinámica no linear discreta devido a Grobman y Hartman nos dice que un difeomorfismo de clase C1, F:E --> E, con E espacio Banach p punto fijo hiperbólico puede ser topológicamente conjugado para lineal Λ=DF(p) (en una vecindad p). Este trabajo tiene como objetivo llenar todos los vacíos completar las pruebas encontradas el pre-print Belintskii-Rayskin , donde da ...

Discretizations and Grobman-Hartman Lemma, discretizations and the hierarchy of invariant manifolds about equilibria are considered. For one-step methods, it is proved that the linearizing conjugacy for ordinary differential equations in Grobman-Hartman Lemma is, with decreasing stepsize, the limit of the linearizing conjugacies of the discrete systems obtained via time-discretizations. Similar...

This work is devoted to the stability of random-switching systems of differential equations. After presenting the formulation of random-switching systems, the notion of stability is recalled, and sufficient conditions in terms of the Liapunov function are presented. Then easily verifiable conditions for stability and instability of systems arising in approximation are established. Using a logar...

Given a smooth closed manifold M , the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. Its homology reproduces singular homology ofM . The geometric approach presented here was developed in [We-93] and is based on...

Due to the nonlinear and nonminimum phase characteristics of buck-boost converter, design its controller has always been a challenging problem. In this paper, multi-index feedback linearization control strategy is proposed converter. Firstly, by constructing an appropriate output function, original system mapped into combination linear subsystem subsystem. Then, according structural these two s...

As one of the seven open problems in the addendum to their 1989 book Computability in Analysis and Physics [21], Pour-El and Richards asked, “What is the connection between the computability of the original nonlinear operator and the linear operator which results from it?” Yet at present, systematic studies of the issues raised by this question seem to be missing from the literature. In this pa...

We consider a hyperbolic diffeomorphism in a Banach space with a hyperbolic fixed point 0 and a linear part Λ. We define σ(Λ) ∈ (0, 1], and prove that for any α < σ(Λ) the diffeomorphism admits local α-Hölder linearization.