Asian Journal of Mathematics

Volume 23 (2019)

Number 3

The genericity of Arnold diffusion in nearly integrable Hamiltonian systems

Pages: 401 – 438



Chong-Qing Cheng (Department of Mathematics, Nanjing Univerisity, Nanjing, China)


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


dynamical instability, Arnold diffusion

2010 Mathematics Subject Classification

37D05, 37J40

This work is supported by NNSF of China (No.11790272 and No.11631006) and the program PAPD of Jiangsu Province, China.

Received 1 September 2017

Accepted 8 December 2017

Published 9 July 2019