Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems
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Publication:2112931
DOI10.1016/j.chaos.2022.112345zbMath1504.37061OpenAlexW4283733150MaRDI QIDQ2112931
Archana Neupane Timsina, Jason D. Mireles James
Publication date: 12 January 2023
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.chaos.2022.112345
periodic orbitsinvariant manifoldscomputational methodsparameterization methodimplicitly defined dynamical systems
Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Computational methods for invariant manifolds of dynamical systems (37M21)
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- The parameterization method for invariant manifolds. From rigorous results to effective computations
- Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case.
- Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra
- Quadratic volume-preserving maps: (Un)stable manifolds, hyperbolic dynamics, and vortex-bubble bifurcations
- A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities
- Computation of whiskered invariant tori and their associated manifolds: new fast algorithms
- Chaotic equilibria in models with backward dynamics
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms
- Computation of maximal local (un)stable manifold patches by the parameterization method
- Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces
- Computational chaos - a prelude to computational instability
- A two-dimensional mapping with a strange attractor
- Chaotic dynamics in a cash-in-advance economy
- Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study
- Homoclinic structures in infinite-dimensional systems
- Noninvertibility and the structure of basins of attraction in a model adaptive control system
- Homoclinic tangles for noninvertible maps
- Hyperbolic sets for noninvertible maps and relations
- Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown
- Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case
- Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
- An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations
- Perturbation theory for linear operators.
- Parameterization of unstable manifolds for DDEs: formal series solutions and validated error bounds
- A functional analytic approach to validated numerics for eigenvalues of delay equations
- Stable manifolds to bounded solutions in possibly ill-posed PDEs
- Discretization and implicit mapping dynamics
- The parameterization method for one-dimensional invariant manifolds of higher-dimensional parabolic fixed points
- A KAM theory for conformally symplectic systems: efficient algorithms and their validation
- The parameterization method for invariant manifolds. III: Overview and applications
- Inverse limits and an implicitly defined difference equation from economics
- A rigorous implicit \(C^1\) Chebyshev integrator for delay equations
- Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps
- Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence
- Validated Computation of Heteroclinic Sets
- Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
- Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications
- Response Solutions to Quasi-Periodically Forced Systems, Even to Possibly Ill-Posed PDEs, with Strong Dissipation and any Frequency Vectors
- A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
- Inverse limits, economics, and backward dynamics;Límites inversos, Economía y Dinámica Regresiva
- Computation of Heteroclinic Arcs with Application to the Volume Preserving Hénon Family
- Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
- Quadratic volume-preserving maps
- On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps
- The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
- The parameterization method for invariant manifolds II: regularity with respect to parameters
- Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits
- High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps
- Oscillation and Chaos in Physiological Control Systems
- KAM theory without action-angle variables
- Invariant Manifolds for Analytic Difference Equations
- Pseudospectral Approximation of Hopf Bifurcation for Delay Differential Equations
- Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form
- A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
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