1 citations · 3 across the 17 of their papers we have counts for
22 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…
Multistability in the Duffing--Holmes oscillator: basins of antiperiodic, periodic, and chaotic attractors and their relative volumes
Arturo C. Marti, Edson D. Leonel
The periodically driven Duffing--Holmes oscillator is strongly multistable: for the same forcing amplitude and frequency, periodic, chaotic, and antiperiodic attractors coexist, ea…
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…
A Symplectic Map Approach to Magnetic Field-Line Dynamics in Tokamaks
Diego F. M. Oliveira, Edson D. Leonel
Magnetic field-line transport in tokamaks is governed by the interplay between chaotic dynamics and invariant phase-space structures that act as partial transport barriers. We inve…
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…
Recurrence and anti-recurrence patterns reveal an antiperiodic fingerprint that survives into chaos in the Duffing--Holmes oscillator
Arturo C. Marti, Edson D. Leonel
The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive. When this sym…
Antiperiodicity in the Duffing--Holmes oscillator: symmetry origin, parity selection, and transitions
Arturo C. Marti, Edson D. Leonel
We investigate the origin and distribution of antiperiodicity --- oscillations satisfying --- in the periodically driven Duffing--Holmes oscillator, combining analyt…
Recurrence time entropy and weak chaos in Hamiltonian flows
Matheus Rolim Sales, Leonardo Costa de Souza, Iberê Luiz Caldas +2
Stickiness in mixed Hamiltonian systems causes chaotic trajectories to remain temporarily trapped near regular structures, making it difficult to distinguish regular, weakly chaoti…
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…
Jacobian determinant as a deformation field in static billiards
Anne Kétri P. da Fonseca, André L. P. Livorati, Rene O. Medrano-T +2
We develop a deformation-based framework for analyzing static billiard systems through the Jacobian determinant computed in noncanonical angular coordinates. Although these systems…
Scaling invariance: a bridge between geometry, dynamics and criticality
Edson D. Leonel, Diego F. M. Oliveira
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear…
Describing a Universal Critical Behavior in a transition from order to chaos
Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo +2
We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deforma…
Universal Second-Order Phase Transition from Integrability to Chaos
Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo +2
We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary . For , the phase space is {\it f…
A phenomenological description of critical slowing down at period-doubling bifurcations
Edson D. Leonel, João P. C. Ferreira, Diego F. M. Oliveira
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expa…
Convergence Dynamics and Scaling Laws in the Dissipative Relativistic Kicked Rotator
Daniel Borin, Danilo S. Rando, Edson D. Leonel +1
We investigate the convergence dynamics of this system near period-doubling bifurcations by combining analytical derivations and large-scale numerical simulations. At the bifurcati…
Scaling invariance for the diffusion coefficient in a billiard system
Anne Kétri P. da Fonseca, Diego F. M. Oliveira, Edson D. Leonel
We investigated the unbounded diffusion observed in a time-dependent oval-shaped billiard and its suppression owing to inelastic collisions with the boundary. The main focus is on…
Symmetry breaking in time-dependent billiards
Anne Kétri Pasquinelli da Fonseca, Edson Denis Leonel
We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, a…
Rare events for low energy domain in bouncing ball model
Edson D. Leonel, Diego F. M. Oliveira
The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control pa…
Discussing a transition from bounded to unbounded energy in a time-dependent billiard
Anne Kétri P. da Fonseca, Felipe Augusto O. Silveira, Célia M. Kuwana +2
We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed st…
Scaling invariance for the diffusion coefficient in a dissipative standard mapping
Edson D. Leonel, Celia M. Kuwana, Diego F. M. Oliveira
The unbounded diffusion observed for the standard mapping in a regime of high nonlinearity is suppressed by dissipation due to the violation of Liouville's theorem. The diffusion c…
Scaling Laws and Convergence Dynamics in a Dissipative Kicked Rotator
Danilo S. Rando, Edson D. Leonel, Diego F. M. Oliveira
The kicked rotator model is an essential paradigm in nonlinear dynamics, helping us understand the emergence of chaos and bifurcations in dynamical systems. In this study, we analy…