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Flow map parameterization methods for invariant tori in quasi-periodic Hamiltonian systems
Álvaro Fernández, Alex Haro, Josep-Maria Mondelo
The purpose of this paper is to present a method to compute parameterizations of invariant tori and bundles in non-autonomous quasi-periodic Hamiltonian systems. We generalize flow…
Flow map parameterization methods for invariant tori in Hamiltonian systems
Alex Haro, Josep-Maria Mondelo
The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic…
Non-twist tori in conformally symplectic systems
Renato Calleja, Marta Canadell, Alex Haro
Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that tran…
Effective bounds for the measure of rotations
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
A fundamental question in Dynamical Systems is to identify regions of phase/parameter space satisfying a given property (stability, linearization, etc). Given a family of analytic…
A-posteriori KAM theory with optimal estimates for partially integrable systems
Alex Haro, Alejandro Luque
In this paper we present a-posteriori KAM results for existence of -dimensional isotropic invariant tori for -DOF Hamiltonian systems with additional independent first…