[HTML][HTML] Thirty years of turnstiles and transport
JD Meiss - Chaos: An Interdisciplinary Journal of Nonlinear …, 2015 - pubs.aip.org
To characterize transport in a deterministic dynamical system is to compute exit time
distributions from regions or transition time distributions between regions in phase space …
distributions from regions or transition time distributions between regions in phase space …
The parameterization method for invariant manifolds
Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …
simple solutions, such as equilibria and periodic orbits, together with their corresponding …
Rigorous computer-assisted application of KAM theory: a modern approach
In this paper, we present and illustrate a general methodology to apply KAM theory in
particular problems, based on an a posteriori approach. We focus on the existence of real …
particular problems, based on an a posteriori approach. We focus on the existence of real …
Birkhoff averages and rotational invariant circles for area-preserving maps
Rotational invariant circles of area-preserving maps are an important and well-studied
example of KAM tori. John Greene conjectured that the locally most robust rotational circles …
example of KAM tori. John Greene conjectured that the locally most robust rotational circles …
Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families
of unstable periodic orbits break up into whiskered tori, with most tori persisting into the …
of unstable periodic orbits break up into whiskered tori, with most tori persisting into the …
Computation of maximal local (un) stable manifold patches by the parameterization method
In this work we develop some automatic procedures for computing high order polynomial
expansions of local (un) stable manifolds for equilibria of differential equations. Our method …
expansions of local (un) stable manifolds for equilibria of differential equations. Our method …
[HTML][HTML] Fourier–Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation
C Reinhardt, JDM James - Indagationes Mathematicae, 2019 - Elsevier
We study polynomial expansions of local unstable manifolds attached to equilibrium
solutions of parabolic partial differential equations. Due to the smoothing properties of …
solutions of parabolic partial differential equations. Due to the smoothing properties of …
Flow map parameterization methods for invariant tori in quasi-periodic Hamiltonian systems
Á Fernández-Mora, A Haro, JM Mondelo - SIAM Journal on Applied …, 2024 - SIAM
The aim of this paper is to present a method to compute parameterizations of partially
hyperbolic invariant tori and their invariant bundles in nonautonomous quasi-periodic …
hyperbolic invariant tori and their invariant bundles in nonautonomous quasi-periodic …
Computation of quasiperiodic normally hyperbolic invariant tori: rigorous results
M Canadell, À Haro - Journal of Nonlinear Science, 2017 - Springer
The development of efficient methods for detecting quasiperiodic oscillations and computing
the corresponding invariant tori is a subject of great importance in dynamical systems and …
the corresponding invariant tori is a subject of great importance in dynamical systems and …
Flow map parameterization methods for invariant tori in Hamiltonian systems
A Haro, JM Mondelo - … in Nonlinear Science and Numerical Simulation, 2021 - Elsevier
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 …
Hamiltonian systems combining flow map methods, parameterization methods, and …