Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
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 homoclin...
| Authors: | , , , |
|---|---|
| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/194449 |
| Online Access: | https://hdl.handle.net/2445/194449 |
| Access Level: | Open access |
| Keyword: | Teoria de la bifurcació Sistemes dinàmics diferenciables Equacions diferencials ordinàries Bifurcation theory Differentiable dynamical systems Ordinary differential equations |
| Summary: | 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. |
|---|