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arXiv · 2102.06436

Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds

Maciej J. Capinski·Jorge Gonzalez·Jean-Pierre Marco·J. D. Mireles James
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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.

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Maciej J. Capinski, Jorge Gonzalez, Jean-Pierre Marco, J. D. Mireles James. 2021-02-12. Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds. https://doi.org/10.1016/j.cnsns.2021.105970

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