# Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders

Source: [Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders](<https://www.sota2.com/research/paper/68fa53971e209131ce984a38>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:32:14.678Z

Authors: Patrick Bernard, K Kaloshin, K Zhang

Published: 2017-01-19T14:49:53.000Z

## Abstract

We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\\epsilon$H1($\\theta$, p, t), $\\theta$ $\\in$ T n , p $\\in$ B n , t $\\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly convex H0. We show that for a "generic" $\\epsilon$H1, there exists an orbit ($\\theta$, p)(t) satisfying p(t) -- p(0) {\\textgreater} l(H1) {\\textgreater} 0, where l(H1) is independent of $\\epsilon$. The diffusion orbit travels along a co-dimension one resonance , and the only obstruction to our construction is a finite set of additional resonances. For the proof we use a combination geometric and variational methods, and manage to adapt tools which have recently been developed in the a priori unstable case.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1701.05445>)

[PDF](<https://arxiv.org/pdf/1701.05445.pdf>)