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

作者：Bessa Mario^*; Rodrigues Alexandre A P

来源：Journal of Differential Equations, 2016, 261(2): 1176-1202.

DOI：10.1016/j.jde.2016.03.040

• Heteroclinic bifurcations
• Tangencies
• Generalized Cocoon bifurcations
• Chirality
• Elliptic solutions

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.

• 出版日期2016-7-15