Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions

Bessa, Mário; Rodrigues, Alexandre A. P.

http://hdl.handle.net/10400.2/13843

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
JDE7.pdf		587.36 KB	Adobe PDF	Download

Send Feedback

Authors

Bessa, Mário

Rodrigues, Alexandre A. P.

Abstract(s)

This paper presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a conservative Bykov cycle where trajectories turn in opposite directions near the two saddle-foci. We show that within the class of divergence-free vector fields that preserve the cycle, tangencies of the invariant manifolds of two hyperbolic saddle-foci densely occur. The global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with non-uniformly hyperbolic suspended horseshoes. A generalized version of the Cocoon bifurcations for conservative systems is obtained.

Keywords

Heteroclinic bifurcations Tangencies Generalized Cocoon bifurcations Chirality Elliptic solutions

URI

http://hdl.handle.net/10400.2/13843

Citation

M. Bessa, A. Rodrigues, Dynamics of conservative Bykov cycles: Tangencies, generalized Cocoon bifurcations and elliptic solutions, 261, 2, 1176-1202, 2016