NONORIENTABLE MANIFOLDS IN THREE-DIMENSIONAL VECTOR FIELDS

DOI10.1142/S0218127403006777zbMath1056.37022OpenAlexW2006903827WikidataQ114476427 ScholiaQ114476427MaRDI QIDQ4653798

Hinke M. Osinga

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127403006777

zbMATH Keywords

bifurcationMöbius stripVector fieldnonorientable invariant manifold

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Invariant manifold theory for dynamical systems (37D10)

Related Items (8)

Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study ⋮ A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS ⋮ Rate-induced tipping: thresholds, edge states and connecting orbits ⋮ Computation of maximal local (un)stable manifold patches by the parameterization method ⋮ Global invariant manifolds near a Shilnikov homoclinic bifurcation ⋮ Saddle Invariant Objects and Their Global Manifolds in a Neighborhood of a Homoclinic Flip Bifurcation of Case B ⋮ LOR for Analysis of Periodic Dynamics: A One-Stop Shop Approach ⋮ Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

Cites Work

• A two-dimensional mapping with a strange attractor
• Local and global behavior near homoclinic orbits
• Asymptotic chaos
• Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study
• Growing 1D and quasi-2D unstable manifolds of maps
• Algorithms for computing normally hyperbolic invariant manifolds
• Constructing dynamical systems having homoclinic bifurcation points of codimension two
• Two-dimensional invariant manifolds and global bifurcations: Some approximation and visualization studies
• Two-dimensional global manifolds of vector fields
• Deterministic Nonperiodic Flow
• Death of period-doublings: Locating the homoclinic-doubling cascade

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