The parameterization method for invariant manifolds. III: Overview and applications

From MaRDI portal
Publication:2575613

DOI10.1016/j.jde.2004.12.003zbMath1101.37019OpenAlexW2036319645MaRDI QIDQ2575613

Xavier Cabré, Ernest Fontich, Rafael de la Llave

Publication date: 5 December 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/910




Related Items (only showing first 100 items - show all)

Parameterization of invariant manifolds for periodic orbits. II: A posteriori analysis and computer assisted error boundsAnalytical and numerical manifolds in a symplectic 4-D mapComputing stable hierarchies of fiber bundlesConstruction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case.HIGH-ORDER BISECTION METHOD FOR COMPUTING INVARIANT MANIFOLDS OF TWO-DIMENSIONAL MAPSParameterization of unstable manifolds for DDEs: formal series solutions and validated error boundsFourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validationStudy of the ejection/collision orbits in the spatial RTBP using the McGehee regularizationComputing (un)stable manifolds with validated error bounds: non-resonant and resonant spectraParameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementationStochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapyConnecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of ExistenceSensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint methodBeyond the Melnikov method: A computer assisted approachValidated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbitsParameterization method for unstable manifolds of delay differential equationsHigh-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problemQuadratic volume-preserving maps: (Un)stable manifolds, hyperbolic dynamics, and vortex-bubble bifurcationsBeyond the Melnikov method. II: Multidimensional settingNonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reductionThe parameterization method for center manifoldsHigh-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of MapsHomoclinic points of 2D and 4D maps via the parametrization methodContinuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proofInvariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillatorsChaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theoremRigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractorConstruction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic caseFourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error boundsValidated numerics for continuation and bifurcation of connecting orbits of mapsComputation of maximal local (un)stable manifold patches by the parameterization methodA note on the convergence of parametrised non-resonant invariant manifoldsDynamics of waves and patterns. Abstracts from the workshop held August 8--14, 2021 (hybrid meeting)Analytic enclosure of the fundamental matrix solution.Validated Computation of Heteroclinic SetsComputer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbitsDifferentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanationsResonant tori, transport barriers, and chaos in a vector field with a Neimark-Sacker bifurcationAnalytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error BoundsPhase-amplitude dynamics in terms of extended response functions: invariant curves and Arnold tonguesTransition state theory with quasi-periodic forcingNumerical integration of high-order variational equations of ODEsCenter Manifold Theory in the Context of Infinite One-Dimensional LatticesLocalized stable manifolds for whiskered tori in coupled map lattices with decaying interactionGlobal phase-amplitude description of oscillatory dynamics via the parameterization methodAnalytical invariant manifolds near unstable points and the structure of chaosPolynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error boundsPhase reduction and phase-based optimal control for biological systems: a tutorialNAVIER AND STOKES MEET POINCARÉAND DULACRigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev seriesDirect computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structuresOn polynomial forms of nonlinear functional differential equationsRigorous numerics for ODEs using Chebyshev series and domain decompositionOn areas of attraction and repulsion in finite time dynamical systems and their numerical approximationComplexity in a Hybrid van der Pol SystemComputer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fieldsGevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed pointsPhase-amplitude response functions for transient-state stimuliEfficient representation of invariant manifolds of periodic orbits in the CRTBPAutomatic differentiation for Fourier series and the radii polynomial approachHomoclinic dynamics in a spatial restricted four-body problem: blue skies into Smale horseshoes for vertical Lyapunov familiesSpatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existenceHomoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution setAsymptotic dynamics of a difference equation with a parabolic equilibriumHigh-order parameterization of (un)stable manifolds for hybrid maps: implementation and applicationsGlobal computation of phase-amplitude reduction for limit-cycle dynamicsPolynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problemA geometric approach to phase response curves and its numerical computation through the parameterization methodCritical homoclinics in a restricted four-body problem: numerical continuation and center manifold computationsFlow map parameterization methods for invariant tori in Hamiltonian systemsA smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearitiesGlobal Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative PerturbationsRecent results on the dynamics of higher-dimensional Hénon mapsComputing Invariant Sets of Random Differential Equations Using Polynomial ChaosDifferentiable invariant manifolds of nilpotent parabolic pointsUsing invariant manifolds to capture an asteroid near the \(L_3\) point of the Earth-Moon bicircular modelParameterization Method for Unstable Manifolds of Standing Waves on the LineAnalytic prediction of isolated forced response curves from spectral submanifoldsInvariant manifolds of parabolic fixed points. I: Existence and dependence on parametersInvariant manifolds of parabolic fixed points. II: Approximations by sums of homogeneous functionsA Contour Algorithm for Computing Stable Fiber Bundles of Nonautonomous, Noninvertible MapsWhiskered parabolic tori in the planar \((n+1)\)-body problemValidated computations for connecting orbits in polynomial vector fieldsComputer assisted proof of drift orbits along normally hyperbolic manifoldsRapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problemsSingularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearityExistence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbitsGlobal dynamics in nonconservative nonlinear Schrödinger equationsMultiple timescales and the parametrisation method in geometric singular perturbation theoryVariational approach to closure of nonlinear dynamical systems: autonomous caseA unified approach to compute foliations, inertial manifolds, and tracking solutionsInvariant manifolds near hyperbolic fixed pointsRigorous validation of stochastic transition pathsFinite element approximation of invariant manifolds by the parameterization methodChebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and ApplicationsStationary Coexistence of Hexagons and Rolls via Rigorous ComputationsDynamics near the invariant manifolds after a Hamiltonian-Hopf bifurcationParameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systemsA numerical method for the approximation of stable and unstable manifolds of microscopic simulatorsStable manifolds under very weak hyperbolicity conditions



Cites Work


This page was built for publication: The parameterization method for invariant manifolds. III: Overview and applications