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arXiv · 1801.02921

The genericity of Arnold diffusion in nearly integrable Hamiltonian systems

Chong-Qing Cheng
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Abstract

In this paper, we prove that the net of transition chain is $δ$-dense for nearly integrable positive definite Hamiltonian systems with 3 degrees of freedom in the cusp-residual generic sense in $C^r$-topology, $r\ge 6$. The main ingredients of the proof existed in \cite{CZ,C17a,C17b}. As an immediate consequence, Arnold diffusion exists among this class of Hamiltonian systems. The question of \cite{C17c} is answered in Section 9 of the paper.

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Chong-Qing Cheng. 2018-01-09. The genericity of Arnold diffusion in nearly integrable Hamiltonian systems. https://arxiv.org/abs/1801.02921

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