Methods and Applications of Analysis

Volume 25 (2018)

Number 3

In Memory of Professor John N. Mather: Part 1 of 3

Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.

Introduction to the study of Arnold diffusion

Pages: 205 – 224



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

Min Zhou (Department of Mathematics, Nanjing University, Nanjing, China)


This article is written for general dynamicists to understand the ideas for the proof of Arnold diffusion conjecture, not in pursuit of rigorousness. Readers need not to be familiar with the variational method based on the Mather theory.


dynamical instability, Arnold diffusion

2010 Mathematics Subject Classification

37D05, 37J40

The authors are supported by NNSF of China (No.11790272 and No.11631006).

Received 29 August 2018

Accepted 4 January 2019

Published 1 November 2019