1st Edition

Lozi Mappings Theory and Applications

By Zeraoulia Elhadj Copyright 2014
    340 Pages 100 B/W Illustrations
    by CRC Press

    This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable for such analysis. The book is not only a good introduction to the Lozi map and its generalizations, it also summarizes of important concepts in dynamical systems theory such as hyperbolicity, SRB measures, attractor types, and more.

    List of Figures

    Comprehensive Review of Hyperbolicity, Ergodicity, and Chaos
    Entropies and statistical properties of chaotic attractors
    Classification of strange attractors of dynamical systems
    Reality of Chaos in the Hénon Mapping
    Measuring chaos in the Hénon map
    Bifurcations phenomena in the Hénon mappings
    Hénon attractor is a quasi-attractor
    Compound windows of the Hénon-map
    The existence of infi nitely many period-doubling bifurcations
    Dynamical Properties of the Lozi Mappings
    Introduction to chaos via the Lozi maps
    Ergodic properties of the Lozi mappings
    Grammatical complexity of the Lozi mappings
    Admissibility conditions for symbolic sequences of the Lozi map
    Existence of strange attractor for b > 0
    Existence of strange attractor for b < 0
    Rigorous proof of chaos in the Lozi map using the theory of transversal heteroclinic cycles
    Geometric structure of strange attractors in the Lozi map
    Parameter-shifted shadowing property of Lozi maps
    The basin of attraction of Lozi mapping
    Relations between the forwards limit sets and the strange attractor
    Topological entropy of the Lozi maps
    Dynamical Properties of Modified and Generalized Lozi Mappings
    Simple piecewise linear models for the zones of instability
    Rigorous calculation of fractal dimension of a strange attractor
    The piecewise linear noodle map
    Generalized hyperbolic attractors
    Global periodicity property of the generalization Lozi mappings
    Generalized discrete Halanay inequality and the global stability of Lozi mapping
    Global behaviors of some max difference equations
    Generalized piecewise-linear area-preserving plane maps
    Smooth versions of the Lozi mappings
    Maps with border-collision period doubling scenario
    Rigorous proof of chaos in a 2-D piecewise linear map
    Occurrence of chaos via different routes
    Generating multifold chaotic attractors
    A new simple 2-D piecewise linear map
    The discrete hyperchaotic double scroll
    Piecewise smooth maps of the plane and robust chaos
    Real and Mathematical Applications of Lozi Mappings
    The Lozi mappings in control theory
    The Lozi mappings in synchronization theory
    The Lozi mappings and secure communications
    The Lozi mappings in game theory
    The Lozi mappings and evolutionary algorithms
    The Lozi mappings and fuzzy modeling of an experimental thermal-vacuum system


    Elhadj, Zeraoulia