Self-similarity of the bandcount adding structures: calculation by map replacement

DOI10.1134/S1560354710060055zbMath1209.37044OpenAlexW1969450168WikidataQ57627341 ScholiaQ57627341MaRDI QIDQ2430936

Laura Gardini, Viktor Avrutin, Michael Schanz

Publication date: 8 April 2011

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354710060055

zbMATH Keywords

chaotic attractorscrisis bifurcationspiecewise-linear mapsbandcount adding and doublingself-similarity and renormalization

Mathematics Subject Classification ID

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Bifurcations of singular points in dynamical systems (37G10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20) Dynamical aspects of attractors and their bifurcations (37G35)

Related Items (7)

Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map ⋮ Bandcount adding structure and collapse of chaotic attractors in a piecewise linear bimodal map ⋮ Analysis of stable periodic orbits in the one dimensional linear piecewise-smooth discontinuous map ⋮ Nonsmooth one-dimensional maps: some basic concepts and definitions ⋮ Bandcount incrementing scenario revisited and floating regions within robust chaos ⋮ The Period Adding and Incrementing Bifurcations: From Rotation Theory to Applications ⋮ Bifurcations and Chaos for 2D Discontinuous Dynamical Model of Financial Markets

Cites Work

• On finite limit sets for transformations on the unit interval
• CALCULATION OF BIFURCATION CURVES BY MAP REPLACEMENT
• On the fully developed bandcount adding scenario
• Crises, sudden changes in chaotic attractors, and transient chaos
• Robust Chaos
• On detection of multi-band chaotic attractors
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