Instability of periodic orbits by Conley–Zehnder index theory
Authors:
Yanxia Deng and Zhihong Xia
Journal:
Proc. Amer. Math. Soc. 149 (2021), 2461-2472
MSC (2020):
Primary 37J46, 37J51, 37J06, 37J39
DOI:
https://doi.org/10.1090/proc/14253
Published electronically:
March 16, 2021
MathSciNet review:
4246797
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We study the connections between the stability properties, the Morse index, and the Conley–Zehnder index of a periodic orbit in Lagrangian systems. We obtain an extremely simple criterion for linear instability for certain periodic orbits.
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Additional Information
Yanxia Deng
Affiliation:
School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, Guangdong, China, 519082
Email:
dengyx53@mail.sysu.edu.cn
Zhihong Xia
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208
MR Author ID:
271126
Email:
xia@math.northwestern.edu
Received by editor(s):
April 11, 2015
Received by editor(s) in revised form:
December 31, 2016, December 6, 2017, and March 6, 2018
Published electronically:
March 16, 2021
Communicated by:
Nimish Shah
Article copyright:
© Copyright 2021
American Mathematical Society