Circular, elliptic and oval billiards in a gravitational field

dc.contributorUniversidade de São Paulo (USP)
dc.contributorUniversidade de Bristol
dc.contributorUniversidade Estadual Paulista (Unesp)
dc.contributorAbdus Salaam Int Ctr Theoret Phys
dc.creatorCosta, Diogo Ricardo da [UNESP]
dc.creatorDettmann, Carl P.
dc.creatorLeonel, Edson D. [UNESP]
dc.date2015-10-21T20:16:34Z
dc.date2015-10-21T20:16:34Z
dc.date2015-05-01
dc.date.accessioned2023-09-12T06:47:39Z
dc.date.available2023-09-12T06:47:39Z
dc.identifierhttp://www.sciencedirect.com/science/article/pii/S1007570414004316
dc.identifierCommunications In Nonlinear Science And Numerical Simulation. Amsterdam: Elsevier Science Bv, v. 22, n. 1-3, p. 731-746, 2015.
dc.identifier1007-5704
dc.identifierhttp://hdl.handle.net/11449/129051
dc.identifier10.1016/j.cnsns.2014.08.030
dc.identifierWOS:000345700500056
dc.identifier6130644232718610
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8778392
dc.descriptionWe consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regimes is made. The linear stability of fixed points is studied, yielding exact analytical expressions for parameter values at which a period-doubling bifurcation occurs. The dynamics is apparently ergodic at certain energies in all three models, in contrast to the regularity of the circular and elliptic billiard dynamics in the field-free case. This finding is confirmed using a sensitive test involving Lyapunov weighted dynamics. In the last part of the paper a time dependence is introduced in the billiard boundary, where it is shown that for the circular billiard the average velocity saturates for zero gravitational force but in the presence of gravitational it increases with a very slow growth rate, which may be explained using Arnold diffusion. For the oval billiard, where chaos is present in the static case, the particle has an unlimited velocity growth with an exponent of approximately 1/6. (C) 2014 Elsevier B.V. All rights reserved.
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação para o Desenvolvimento da UNESP (FUNDUNESP)
dc.descriptionCenter for Scientific Computing (NCC/GridUNESP) of the Sao Paulo State University (UNESP)
dc.descriptionUniv Sao Paulo, Inst Fis, BR-05508090 Sao Paulo, Brazil
dc.descriptionUniv Bristol, Sch Math, Bristol, Avon, England
dc.descriptionUNESP, Dept Fis, BR-13506900 Rio Claro, SP, Brazil
dc.descriptionAbdus Salaam Int Ctr Theoret Phys, Abdus Salam, I-34151 Trieste, Italy
dc.descriptionUniversidade Estadual Paulista, Departamento de Física, BR-13506900 Rio Claro, SP, Brazil
dc.descriptionFAPESP: 2013/22764-2
dc.descriptionFAPESP: 2012/18962-0
dc.descriptionFAPESP: 2010/52709-5
dc.descriptionFAPESP: 2012/23688-5
dc.format731-746
dc.languageeng
dc.publisherElsevier B.V.
dc.relationCommunications In Nonlinear Science And Numerical Simulation
dc.relation3.181
dc.relation1,372
dc.rightsAcesso restrito
dc.sourceWeb of Science
dc.subjectCircular
dc.subjectElliptic
dc.subjectOval
dc.subjectBilliard
dc.subjectGravitational field
dc.titleCircular, elliptic and oval billiards in a gravitational field
dc.typeArtigo


Este ítem pertenece a la siguiente institución