BIFURCATIONS OF STABLE SETS IN NONINVERTIBLE PLANAR MAPS

DOI10.1142/S0218127405012466zbMath1085.37036OpenAlexW1991658172WikidataQ114476428 ScholiaQ114476428MaRDI QIDQ5318376

J. P. England, Bernd Krauskopf, Hinke M. Osinga

Publication date: 26 September 2005

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

Full work available at URL: https://doi.org/10.1142/s0218127405012466

zbMATH Keywords

bifurcationbasin of attractionstable setcritical curvenoninvertible planar map

Mathematics Subject Classification ID

Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical aspects of attractors and their bifurcations (37G35) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30)

Related Items (5)

Global stability and bifurcations of perturbed Gumowski–Mira difference equation ⋮ BIFURCATIONS OF THE GLOBAL STABLE SET OF A PLANAR ENDOMORPHISM NEAR A CUSP SINGULARITY ⋮ Novel routes to chaos through torus breakdown in non-invertible maps ⋮ A Contour Algorithm for Computing Stable Fiber Bundles of Nonautonomous, Noninvertible Maps ⋮ Chaos and Wild Chaos in Lorenz-Type Systems

Uses Software

• DSTool

Cites Work

• Recurrences and discrete dynamic systems
• Noninvertibility and the structure of basins of attraction in a model adaptive control system
• BASIN BIFURCATIONS OF TWO-DIMENSIONAL NONINVERTIBLE MAPS: FRACTALIZATION OF BASINS
• NONINVERTIBLE TWO-DIMENSIONAL MAPS ARISING IN RADIOPHYSICS
• On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps
• Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse
• COMPLEX PATTERNS ON THE PLANE: DIFFERENT TYPES OF BASIN FRACTALIZATION IN A TWO-DIMENSIONAL MAPPING
• On the Fractal Structure of Basin Boundaries in Two-Dimensional Noninvertible Maps
• An Algorithm for the Computation of Preimages in Noninvertible Mappings
• Basin Properties in Two-Dimensional Noninvertible Maps

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