Non-twist invariant circles in conformally symplectic systems
Por:
Calleja, Renato, Canadell, Marta, Haro, Alex
Publicada:
1 may 2021
Resumen:
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.
(c) 2021 Elsevier B.V. All rights reserved.
Filiaciones:
Calleja, Renato:
Department of Mathematics and Mechanics, IIMAS, National Autonomous University of Mexico (UNAM), Apdo. Postal 20-126Mexico D.F. C.P. 04510, Mexico
Natl Autonomous Univ Mexico UNAM, Dept Math & Mech, IIMAS, Apdo Postal 20-126, Mexico City 04510, DF, Mexico
Canadell, Marta:
Wallapop, Av. Meridiana, Barcelona, 89 - P.6 08026, Spain
Wallapop, Av Meridian 89-P6, Barcelona 08026, Spain
Haro, Alex:
Departament de Matemàtiques i Informàtica, Universitat de Barcelona & BGSMath, Gran Via 585, Barcelona, 08007, Spain
Univ Barcelona & BGSMath, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain
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