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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Instability of periodic orbits by Conley–Zehnder index theory
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by Yanxia Deng and Zhihong Xia PDF
Proc. Amer. Math. Soc. 149 (2021), 2461-2472 Request permission


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:
  • Zhihong Xia
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
  • MR Author ID: 271126
  • Email:
  • 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
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2461-2472
  • MSC (2020): Primary 37J46, 37J51, 37J06, 37J39
  • DOI:
  • MathSciNet review: 4246797