Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150633 |
| Acceso en línea: | https://ddd.uab.cat/record/150633 https://dx.doi.org/urn:doi:10.1016/j.na.2012.10.017 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial differential equation Bifurcation of limit cycles Shape Number Location and period of limit cycles |
| Sumario: | In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and we apply it to know, up to any order, the shape of the limit cycles bifurcating from the period annulus of the class of radial Hamiltonians. We write any solution, in polar coordinates, as a power series expansion in terms of the small parameter. This expansion is also used to give the period of the bifurcated periodic solutions. We present the concrete expression of the solutions up to third order of perturbation of Hamiltonians of the form H = H(r). Necessary and sufficient conditions that show if a solution is simple or double are also presented. |
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