Weak type heterodimensional cycle bifurcation with orbit-flip
type: Item
instance of: scholarly article
title: Weak type heterodimensional cycle bifurcation with orbit-flip
zbMATH Open document ID: 1242.34081
published in: Science China. Mathematics
publication date: 2012-01-16T00:00:00Z
review text: The paper presents the study of the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit. The main approach is the local moving frame method established in [\textit{D.~Zhu}, ``Problems in homoclinic bifurcation with higher dimensions'', Acta Math. Sin., New Ser. 14, No. 3, 341--352 (1998; Zbl 0932.37032)]. For two subcases, sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit are obtained. Bifurcation surfaces and existence regions are located via bifurcation analysis. For the third subcase, both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for a persistent heterodimensional cycle and multiple periodic orbits are established. An analytical example is presented to illustrate the main results.
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5997887
zbMATH Keywords: local moving frame
zbMATH Keywords: weak heterodimensional cycle
zbMATH Keywords: orbit-flip
zbMATH Keywords: bifurcation analysis
author: Qiuying Lu
author: Deming Zhu
author: Fengjie Geng
MaRDI profile type: Publication
full work available at URL: s11425-011-4167-z
OpenAlex ID: W2030595735
cites work: Q4519407
cites work: Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms
cites work: Homoclinic bifurcation at resonant eigenvalues
cites work: Nonconnected heterodimensional cycles: bifurcation and stability
cites work: Heterodimensional cycles, partial hyperbolicity and limit dynamics
cites work: Q4037995
cites work: Bifurcations of heterodimensional cycles with two saddle points
cites work: Smooth Linearization Near a Fixed Point
cites work: Degenerated homoclinic bifurcations with higher dimensions
cites work: Bifurcations of rough heteroclinic loops with three saddle points
cites work: Degenerate bifurcations of nontwisted heterodimensional cycles with codimension 3
cites work: HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP
cites work: Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
cites work: Contributions to the stability conjecture
cites work: Diffeomorphisms with infinitely many sinks
cites work: Q4084984
cites work: Q4941620
cites work: Q4003408
cites work: Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
cites work: On the Structure of Local Homeomorphisms of Euclidean n-Space, II
cites work: Branching of double pulse solutions from single pulse solutions in nerve axon equations
cites work: Problems in homoclinic bifurcation with higher dimensions
cites work: CODIMENSION 3 HOMOCLINIC BIFURCATION OF ORBIT FLIP WITH RESONANT EIGENVALUES CORRESPONDING TO THE TANGENT DIRECTIONS
DOI: 10.1007/S11425-011-4167-Z
description: scientific article; zbMATH DE number 5997887