Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds
arXiv:2102.06436 · doi:10.1016/j.cnsns.2021.105970
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.
arXiv comment30 pages, 6 figures
References in corpus (5)
- Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
- 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
- Improved exponential stability for near-integrable quasi-convex Hamiltonians
- Improved stability for analytic quasi-convex nearly integrable systems and optimal speed of Arnold diffusion