Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
| Autor: | J. Tomás Lázaro, Marina Gonchenko, Sergey Gonchenko, Amadeu Delshams |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Mathematics::Dynamical Systems Applied Mathematics 010102 general mathematics Mathematical analysis Dynamics (mechanics) Tangent Fixed point 01 natural sciences 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics Quadratic equation Stability theory 0103 physical sciences Discrete Mathematics and Combinatorics Periodic orbits Homoclinic orbit 0101 mathematics Analysis Saddle |
| Zdroj: | Discrete & Continuous Dynamical Systems - A. 38:4483-4507 |
| ISSN: | 1553-5231 |
| DOI: | 10.3934/dcds.2018196 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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