Existence of heterodimensional cycles near shilnikov loops in systems with
a Z(2) symmetry
a Z(2) symmetry
File(s)1512.01280v3.pdf (716.37 KB)
Accepted version
Author(s)
Li, D
Turaev, DV
Type
Journal Article
Abstract
We prove that a pair of heterodimensional cycles can be born at the bifurcations of a pair of Shilnikov loops (homoclinic loops to a saddle-focus equilibrium) having a one-dimensional unstable manifold in a volume-hyperbolic flow with a Z2 symmetry. We also show that these heterodimensional cycles can belong to a chain-transitive attractor of the system along with persistent homoclinic tangency.
Date Issued
2017-04-01
Date Acceptance
2017-04-01
Citation
Discrete and Continuous Dynamical Systems - Series A, 2017, 37 (8), pp.4399-4437
ISSN
1078-0947
Publisher
American Institute of Mathematical Sciences
Start Page
4399
End Page
4437
Journal / Book Title
Discrete and Continuous Dynamical Systems - Series A
Volume
37
Issue
8
Copyright Statement
© 2017 American Institute of Mathematical Sciences
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000401074500013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Heterodimensional cycle
homoclinic bifurcation
saddle-focus
homoclinic tangency
chaotic dynamics
strange attractor
SADDLE-FOCUS
CENTER MANIFOLDS
ATTRACTORS
DIFFEOMORPHISMS
BIFURCATION
DIMENSION
DYNAMICS
SET
Publication Status
Published