5 papers
Geometry-induced chaos and scaling near two singular limits of an eye-shaped billiard
Anne Kétri P. da Fonseca, Edson D. Leonel, Diego F. M. Oliveira
We investigate how boundary geometry controls the coexistence of regular and chaotic motion in a static, eye-shaped billiard. A single control parameter continuously deforms the sm…
First-order integrability-breaking phase transitions in dynamical systems
Anne Ketri P. da Fonseca, Marcelo de Almeida Presotto, Diego F. M. Oliveira +1
We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary…
First-Order Transition to Chaos with Critical Slowing Down
Anne Ketri P. da Fonseca, Marcelo de Almeida Presotto, Diego F. M. Oliveira +1
Can the transition from integrability to chaos be discontinuous? We show that it can, and that the resulting first-order dynamical transition coexists with critical slowing down. U…
Integrability-breaking phase transitions in stadium-like billiards
Anne Kétri P. da Fonseca, Edson D. Leonel
We investigate integrability-breaking transitions in two classes of stadium-like billiards with parabolic boundaries. While focusing boundaries generate a mixed phase space in whic…
Critical parameters of an oval billiard with an elliptical component
Anne Kétri P. da Fonseca, Joelson D. V. Hermes, Edson D. Leonel
We explore the critical parameters responsible for the transition from integrability to chaos in a family of billiards combining elliptical and oval deformations. Unlike standard o…