Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations

DOI10.2200/S00373ED1V01Y201107MAS011zbMath1237.37001OpenAlexW2113720055MaRDI QIDQ3090063

Yu Huang, Goong Chen

Publication date: 26 August 2011

Published in: Synthesis Lectures on Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2200/s00373ed1v01y201107mas011

zbMATH Keywords

total variationchaosLyapunov exponentsbifurcationssymbolic dynamicsinterval mapsfractalschaotic dynamical systemsSmale horseshoehomoclinicityrapid fluctuationsordering among periodsSharkovski theoremtime difference equations

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Topological entropy (37B40) Dynamical systems involving maps of the interval (37E05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (13)

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case ⋮ Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations ⋮ Chaotic Oscillations of Solutions of First Order Hyperbolic Systems in 1D with Nonlinear Boundary Conditions ⋮ Chaotic Oscillations of 1D Wave Equation Due to a Generalized Nonlinear Energy-Decay Boundary Condition ⋮ Chaotic oscillations of one-dimensional coupled wave equations with mixed energy transports ⋮ Chaotic behaviors of one dimensional wave equations with van der Pol nonlinear boundary conditions ⋮ A Novel Fixed Point Feedback Approach Studying the Dynamical Behaviors of Standard Logistic Map ⋮ Chaotic Behaviors of One-Dimensional Wave Equations with van der Pol Boundary Conditions Containing a Source Term ⋮ Functional envelopes relative to the point-open topology on a subset ⋮ Abstract similarity, fractals and chaos ⋮ Chaotic dynamics of a 2D hyperbolic PDE with the boundary conditions of superlinear type ⋮ Domain-Structured Chaos in a Hopfield Neural Network ⋮ A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road

This page was built for publication: Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations