32 citations · 58 across the 7 of their papers we have counts for
10 papers
A Modified Parameterization Method for Invariant Lagrangian Tori for Partially Integrable Hamiltonian Systems
Jordi-Lluís Figueras, Alex Haro
In this paper we present an a-posteriori KAM theorem for the existence of an -parameters family of -dimensional isotropic invariant tori with Diophantine frequency vector…
Semi-analytical computation of heteroclinic connections between center manifolds with the parameterization method
Miquel Barcelona, Alex Haro, Josep-Maria Mondelo
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed poi…
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…
On the sharpness of the Rüssmann estimates
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
Estimating the norm of the solution of the linear difference equation plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the soluti…
Rigorous computer assisted application of KAM theory: a modern approach
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
In this paper we present and illustrate a general methodology to apply KAM theory in particular problems, based on an {\em a posteriori} approach. We focus on the existence of real…
Strange Nonchaotic Attractors in Harper Maps
Alex Haro, Joaquim Puig
We study the existence of Strange Nonchaotic Attractors (SNA) in the family of Harper maps, proving that they are typical but not robust in this family. Our approach is based on th…