Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds

Abstract

Normally hyperbolic invariant manifolds theory provides an efficient tool for proving diffusion in dynamical systems. In this paper we develop a methodology for computer assisted proofs of diffusion in a-priori chaotic systems based on this approach. We devise a method, which allows us to validate the needed conditions in a finite number of steps, which can be performed by a computer by means of rigorous-interval-arithmetic computations. We apply our method to the generalized standard map, obtaining diffusion over an explicit range of actions.

30 pages, 6 figures

References in corpus (2)

• CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
• Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders

Cited by in corpus (1)

• Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem