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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
First steps in symplectic and spectral theory of integrable systems
Álvaro Pelayo, San Vũ Ngoc
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian…
math.DS2013
Symplectic theory of completely integrable Hamiltonian systems
Álvaro Pelayo, San Vũ Ngoc
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredi…