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math.DS2023
The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps
Álvaro Pelayo, Fraydoun Rezakhanlou
We take the first steps to develop Conley-Zehnder Theory, as conjectured by Arnold, in the world of probability. As far as we know, this paper provides the first probabilistic theo…
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…