Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/771 |
| Acceso en línea: | https://hdl.handle.net/2117/771 |
| Access Level: | acceso abierto |
| Palabra clave: | Dynamical systems Bifurcation theory Poincare-Melnikov method Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory |
| Sumario: | The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the splitting of separatrices is the so-called Poincaré-Melnikov method, which has several specic features in the case of analytic planar maps. The aim of this talk is to compare the predictions for the splitting of separatrices provided by the Poincaré-Melnikov method, with the analytic and numerical results in a simple example where computations in multiple-precision arithmetic are performed. |
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