Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian

Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian

In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x ˙ = y , y ˙ = x ( x 2 - 1 ) ( x 2 + 1 ) ( x 2 + 2 ) . The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that ther...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) Vol. 2019; no. 2019; pp. 1 - 8
Main Authors: Huang, Weihua, Hu, Xiaochun, Yang, Sumin, Zhu, Hongying
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2019
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Hindawi-Wiley
Subjects:
Annuli
Hamiltonian functions
Perturbation
Saddles
Online Access:Get full text
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Summary:In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x ˙ = y , y ˙ = x ( x 2 - 1 ) ( x 2 + 1 ) ( x 2 + 2 ) . The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at least 3 limit cycles emerging from the period annulus, and 3 limit cycles are near the boundaries.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/5813596