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Hyperbolic Structures in ODE’s and Their Discretization with an Appendix on Differentiability Properties of the Inversion Operator

  • B. M. Garay
Part of the International Centre for Mechanical Sciences book series (CISM, volume 371)

Abstract

We survey some recent results of numerical dynamics centered about hyperbolic structures including structural stability, normally hyperbolic compact invariant manifolds, and topological horseshoes on transversal sections. The presentation itself is followed by a discussion on some of the underlying abstract mathematical theories. The paper ends with results on the inversion operator we have no references for. Proposition b.) stating that “operator φφ −1 as a self-homeomorphism of Diff1 (M) is nowhere differentiable” seems to be new.

Keywords

Composition Operator Invariant Manifold Exponential Dichotomy Hyperbolic Structure Inverse Function Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • B. M. Garay
    • 1
  1. 1.University of TechnologyBudapestHungary

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