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...

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 ...

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.

&#x0D; Em matemática, o termo "não linear" geralmente corresponde a uma análise mais difícil. Uma vez que os sistemas lineares são simples de analisar, maneira importante entender não é descobrir em condições eles podem ser bem aproximados por lineares. A respeito disso, temos um célebre teorema equações diferenciais Grobman [Gro59] e Hartman [Har60a], nos garante campo vetorial classe C1, X : ...

In 34 years of psychiatric practice, no clinical problems have been more intriguing to me than underachievement and self-destructive behavior in exceptionally gifted adolescents and young adults. Early in my career as an associate clinical professor in Tufts University School of Medicine’s Department of Psychiatry, I was stimulated by the challenge of establishing a community-based mental healt...

Contents Chapter 1. Introduction 7 1. Historical sketch 7 a. Homoclinic tangles 7 b. Geodesic flows 8 c. Picking up from Poincaré 8 d. Modern hyperbolic dynamics 9 e. The slowness of the initial development 9 2. Hyperbolic dynamics 10 3. Outline of this survey 10 a. Regularity 11 Chapter 2. Hyperbolic sets and stable manifolds 13 1. Definitions and examples 13 a. Hyperbolic linear maps, adapted...

Variability in the underlying time structure of dynamical systems and its consequences are encountered in a variety of mathematical contexts, though are not always recognized as such. An obvious example is the numerical time-discretization of ordinary differential equations, where the relationship between the behaviour of an approximate discrete-time dynamical system and that of the original co...

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

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...