Miniatura

Fitxers

708628.pdf (6.11 MB)

Tipus de document

Article

Versió

Versió acceptada

Data de publicació

2021-05

Llicència de publicació

cc-by-nc-nd (c) Elsevier B.V., 2021
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/192686

Non-twist invariant circles in conformally symplectic systems

Títol de la revista

Autors

Director/Tutor

ISSN de la revista

Títol del volum

Recurs relacionat

https://doi.org/10.1016/j.cnsns.2021.105695

Resum

Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a conformal factor smaller than 1). It is important to understand the structure and the dynamics on the attractors. It is well-known that, with the aid of parameters, and under suitable non-degeneracy conditions, one can obtain that there is an attractor that is an invariant torus whose internal dynamics is conjugate to a rotation. By analogy with symplectic dynamics, a natural question is establishing appropriate definitions for twist and non-twist invariant tori in conformally symplectic systems. The main goals of this paper are: (a) to establish proper definitions of twist and non-twist invariant tori in families of conformally symplectic systems; (b) to interpret these definitions in terms of dynamical properties; (c) to derive algorithms to compute twist and non-twist invariant tori; (d) to implement these algorithms in examples; (e) to explore the mechanisms of breakdown of twist and non-twist invariant tori. Hence, the last part of the paper is devoted to implementations of the algorithms, illustrating the definitions presented in this paper, and studying robustness properties of invariant tori.

Matèries

Sistemes hamiltonians, Pertorbació (Matemàtica), Equacions diferencials ordinàries, Teoria de l'aproximació

Matèries (anglès)

Hamiltonian systems, Perturbation (Mathematics), Ordinary differential equations, Approximation theory

Citació

Col·leccions

Articles publicats en revistes (Matemàtiques i Informàtica)

Citació

CALLEJA, Renato, CANADELL CANO, Marta, HARO, Àlex. Non-twist invariant circles in conformally symplectic systems. _Communications In Nonlinear Science And Numerical Simulation_. 2021. Vol. 96. [consulta: 6 de febrer de 2026]. ISSN: 1007-5704. [Disponible a: https://hdl.handle.net/2445/192686]

Exportar metadades

JSON - METS

Compartir registre