3 papers
math.DS2024
Bifurcations in the family of billiards associated with the curvature flow
C. Salazar, J. G. Damasceno, M. J. D. Carneiro
We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature (curve-shortening) flow. We obtain the bif…
math.DS2020
A note on Tonelli Lagrangian systems on with positive topological entropy on high energy level
J. G. Damasceno, J. A. G. Miranda, L. G. Perona
In this work we study the dynamical behavior Tonelli Lagrangian systems defined on the tangent bundle of the torus . We prove that the Lag…
math.DS2015
The billiard inside an ellipse deformed by the curvature flow
Josue Damasceno, Mario J. Dias Carneiro, Rafael Ramirez-Ros
The billiard dynamics inside an ellipse is integrable. It has zero topological entropy, four separatrices in the phase space, and a continuous family of convex caustics: the confoc…