Computation of nonautonomous invariant and inertial manifolds

DOI10.1007/s00211-009-0215-9zbMath1169.65116OpenAlexW2092936835MaRDI QIDQ1027738

Martin Rasmussen, Christian Poetzsche

Publication date: 30 June 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-4793

zbMATH Keywords

inexact Newton methodsinvariant manifoldsdiscrete dynamical systemssystems of nonlinear algebraic equationsfiber bundlesHenon mapChafee-Infante equationLyapunov-Perron operatorpopulation dynamical modelsemi-linear nonautonomous difference equations

Mathematics Subject Classification ID

Related Items (8)

Computing stable hierarchies of fiber bundles ⋮ Global error analysis and inertial manifold reduction ⋮ Provably convergent implementations of the subdivision algorithm for the computation of invariant objects ⋮ On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation ⋮ Partial linearization for planar nonautonomous differential equations ⋮ A Contour Algorithm for Computing Stable Fiber Bundles of Nonautonomous, Noninvertible Maps ⋮ Variational approach to closure of nonlinear dynamical systems: autonomous case ⋮ A unified approach to compute foliations, inertial manifolds, and tracking solutions

Uses Software

• GAIO
• NewtonLib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical Taylor expansions for invariant manifolds
• Numerical Taylor expansions of invariant manifolds in large dynamical systems
• A subdivision algorithm for the computation of unstable manifolds and global attractors
• Algorithms for computing normally hyperbolic invariant manifolds
• Approximate Newton methods for nonsmooth equations
• Taylor approximation of invariant fiber bundles for nonautonomous difference equations
• \(C^m\)-smoothness of invariant fiber bundles
• Computing inertial manifolds
• Pullback attracting inertial manifolds for nonautonomous dynamical systems
• On the computation of invariant manifolds of fixed points
• Attractive invariant manifolds under approximation. Inertial manifolds
• Averaging of trajectory attractors of evolution equations with rapidly oscillating terms
• Discrete inertial manifolds
• Computation of integral manifolds for Caratheodory differential equations
• Conewise Linear Systems: Non‐Zenoness and Observability
• Center manifolds of dynamical systems under discretization
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• Semismooth and Semiconvex Functions in Constrained Optimization
• Algorithms for constructing stable manifolds of stationary solutions
• A 'taut string algorithm' for straightening a piecewise linear path in two dimensions
• Solving Nonlinear Equations with Newton's Method
• A Fast Method for Approximating Invariant Manifolds
• Numerical calculation of invariant manifolds for maps
• Global stability in a nonlinear difference-delay equation model of flour beetle population growth
• Numerical continuation of normally hyperbolic invariant manifolds
• A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
• Attractive invariant fiber bundles
• Computing Invariant Manifolds by Integrating Fat Trajectories
• Integral manifolds under explicit variable time-step discretization
• Computation of non-smooth local centre manifolds
• Dynamics of evolutionary equations

This page was built for publication: Computation of nonautonomous invariant and inertial manifolds