Publicação: Time Recurrence Analysis of a Near Singular Billiard
Carregando...
Data
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Mdpi
Tipo
Artigo
Direito de acesso
Acesso aberto
Resumo
Billiards exhibit rich dynamical behavior, typical of Hamiltonian systems. In the present study, we investigate the classical dynamics of particles in the eccentric annular billiard, which has a mixed phase space, in the limit that the scatterer is point-like. We call this configuration the near singular, in which a single initial condition (IC) densely fills the phase space with straight lines. To characterize the orbits, two techniques were applied: (i) Finite-time Lyapunov exponent (FTLE) and (ii) time recurrence. The largest Lyapunov exponent lambda was calculated using the FTLE method, which for conservative systems, lambda > 0 indicates chaotic behavior and lambda = 0 indicates regularity. The recurrence of orbits in the phase space was investigated through recurrence plots. Chaotic orbits show many different return times and, according to Slater's theorem, quasi-periodic orbits have at most three different return times, the bigger one being the sum of the other two. We show that during the transition to the near singular limit, a typical orbit in the billiard exhibits a sharp drop in the value of lambda, suggesting some change in the dynamical behavior of the system. Many different recurrence times are observed in the near singular limit, also indicating that the orbit is chaotic. The patterns in the recurrence plot reveal that this chaotic orbit is composed of quasi-periodic segments. We also conclude that reducing the magnitude of the nonlinear part of the system did not prevent chaotic behavior.
Descrição
Palavras-chave
recurrence time, Slater's theorem, Lyapunov exponent, point scatterer, annular billiard
Idioma
Inglês
Como citar
Mathematical And Computational Applications. Basel: Mdpi, v. 24, n. 2, 16 p., 2019.
