Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies

Abstract

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits.

25 pages, 10 figures

References in corpus (1)

• On dynamics and bifurcations of area-preserving maps with homoclinic tangencies

Cited by in corpus (3)

• On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators
• Dense heteroclinic tangencies near a Bykov cycle
• On three types of dynamics, and the notion of attractor