## 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

## 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.## References

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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
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 2461-2472 - MSC (2020): Primary 37J46, 37J51, 37J06, 37J39
- DOI: https://doi.org/10.1090/proc/14253
- MathSciNet review: 4246797