13 papers
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…
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 {\…
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…