SOME BIFURCATION RESULTS IN NEAR-HAMILTONIAN SYSTEMS WITH FINITE-ORDER SMOOTHNESS

Ci Kong; Maoan Han; Yun Tian; Xianbo Sun

doi:10.11948/20260335

2027 Volume 17 Issue 1

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Ci Kong, Maoan Han, Yun Tian, Xianbo Sun. SOME BIFURCATION RESULTS IN NEAR-HAMILTONIAN SYSTEMS WITH FINITE-ORDER SMOOTHNESS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 579-607. doi: 10.11948/20260335

Citation:

Ci Kong, Maoan Han, Yun Tian, Xianbo Sun. SOME BIFURCATION RESULTS IN NEAR-HAMILTONIAN SYSTEMS WITH FINITE-ORDER SMOOTHNESS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 579-607. doi: 10.11948/20260335

SOME BIFURCATION RESULTS IN NEAR-HAMILTONIAN SYSTEMS WITH FINITE-ORDER SMOOTHNESS

1.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
3.
School of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, China

Author Bio: Email: cikong@zjnu.edu.cn(C. Kong); Email: ytian22@shnu.edu.cn(Y. Tian); Email: xsun@hznu.edu.cn(X. Sun)
Corresponding author: Email: mahan@zjnu.edu.cn(M. Han)
Fund Project: This work was supported by the National Natural Science Foundation of China (No. 12571187)

Abstract

Abstract

This paper presents a systematic survey of bifurcation theory for near-Hamiltonian systems with finite-order smoothness. Unlike the classical $C^{\infty}$ or $C^{\omega}$ framework, we collect some known results on limit cycle bifurcations for planar systems with finite-order smoothness, including Poincaré bifurcation, Hopf bifurcation, homoclinic bifurcation, double homoclinic bifurcation, heteroclinic bifurcation, and bifurcations involving nilpotent singularities. For each type, we summarize the relevant bifurcation theorems on properties of the Melnikov functions and the conditions for the existence and the number of limit cycles that can be produced.
- Limit cycle /
- bifurcation /
- near-Hamiltonian system /
- finite-order smoothness /
- Melnikov function
MSC: 34C05, 34C07, 34C23

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References

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