Toward the calculation of higher-dimensional stable manifolds and stable sets for noninvertible and piecewise-smooth maps

DOI10.1007/s00332-007-9016-4zbMath1167.37039OpenAlexW2071197979MaRDI QIDQ1015412

Danny Fundinger

Publication date: 8 May 2009

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-007-9016-4

zbMATH Keywords

algorithmsnonlinear dynamical systemsstable manifoldadaptive subdivisionglobal stable setnoninvertible map

Mathematics Subject Classification ID

Low-dimensional dynamical systems (37E99) Computational methods for bifurcation problems in dynamical systems (37M20) Approximation methods and numerical treatment of dynamical systems (37M99) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Uses Software

• AnT 4.669

Cites Work

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• A procedure for finding numerical trajectories on chaotic saddles
• A two-dimensional mapping with a strange attractor
• An efficient method for computing invariant manifolds of planar maps
• Growing 1D and quasi-2D unstable manifolds of maps
• A subdivision algorithm for the computation of unstable manifolds and global attractors
• On the computation of invariant manifolds of fixed points
• CALCULATING STABLE AND UNSTABLE MANIFOLDS
• Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields
• Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse
• Chaotic dynamics of a nonlinear density dependent population model
• An Algorithm for the Computation of Preimages in Noninvertible Mappings
• Globalizing Two-Dimensional Unstable Manifolds of Maps
• A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
• Computing Invariant Manifolds by Integrating Fat Trajectories
• ON THE USE OF MATRICES IN CERTAIN POPULATION MATHEMATICS
• An adaptive subdivision technique for the approximation of attractors and invariant measures