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math.DS2013
Poincaré-Birkhoff theorems in random dynamics
Álvaro Pelayo, Fraydoun Rezakhanlou
We propose a generalization of the Poincaré-Birkhoff Theorem on area-preserving twist maps to area-preserving twist maps that are random with respect to an ergodic probability meas…
math.DS2011★ 11 cited
Symplectic bifurcation theory for integrable systems
Alvaro Pelayo, Tudor S. Ratiu, San Vu Ngoc
This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcat…