Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 347-362.doi: 10.1007/s10473-025-0205-8

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BRAKE ORBITS WITH MINIMAL PERIOD ESTIMATES OF FIRST-ORDER ANISOTROPIC HAMILTONIAN SYSTEMS

Xiaofei Zhang1, Chungen Liu2,*   

  1. 1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China;
    2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
  • Received:2022-10-03 Revised:2024-08-19 Online:2025-03-25 Published:2025-05-08
  • Contact: *Chungen Liu, E-mail: liucg@nankai.edu.cn
  • About author:Xiaofei Zhang, E-mail: 835858094@qq.com
  • Supported by:
    The first author's work was supported by the NSFC (12301138), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2021L377) and the Doctoral Scientific Research Foundation of Shanxi Datong University (2018-B-15). The second author's work was supported by the NSFC (12171108).

Abstract: In this paper, the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth, i.e., the Hamiltonian functions may have super-quadratic, sub-quadratic and quadratic behaviors simultaneously in different variable components.

Key words: Hamiltonian system, anisotropic growth, brake orbit, L0-index

CLC Number: 

  • 70H05
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