Dynamics with chaos and fractals

Dynamics with chaos and fractals / Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily.

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable poin...

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Bibliographic Details
Main Author: Akhmet, Marat
Other Authors: Fen, Mehmet Onur, Alejaily, Ejaily Milad
Format: eBook
Language:English
Published: Cham : Springer, 2020.
Series:Nonlinear systems and complexity ; v. 29.
Subjects:
Chaotic behavior in systems.
Fractals.
fractals.
Comportamiento caótico en sistemas
Fractales
Chaotic behavior in systems
Fractals
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Contents
  • 1 Introduction
  • References
  • 2 The Unpredictable Point and Poincaré Chaos
  • 2.1 Preliminaries
  • 2.2 Dynamics with Unpredictable Points
  • 2.3 Chaos on the Quasi-Minimal Set
  • 2.4 Applications
  • 2.5 Notes
  • References
  • 3 Unpredictability in Bebutov Dynamics
  • 3.1 Introduction
  • 3.2 Preliminaries
  • 3.3 Unpredictable Functions
  • 3.4 Unpredictable Solutions of Quasilinear Systems
  • 3.5 Examples
  • 3.6 Notes
  • References
  • 4 Nonlinear Unpredictable Perturbations
  • 4.1 Preliminaries
  • 4.2 An Unpredictable Sequence of the Symbolic Dynamics
  • 4.3 An Unpredictable Solution of the Logistic Map
  • 4.4 An Unpredictable Function
  • 4.5 Unpredictable Solutions of Differential Equations
  • 4.6 Notes
  • References
  • 5 Unpredictability in Topological Dynamics
  • 5.1 Introduction
  • 5.2 Quasilinear Delay Differential Equations
  • 5.3 Quasilinear Discrete Equations
  • 5.4 A Continuous Unpredictable Function via the Logistic Map
  • 5.5 Examples
  • 5.6 A Hopfield Neural Network
  • 5.7 Notes
  • References
  • 6 Unpredictable Solutions of Hyperbolic Linear Equations
  • 6.1 Preliminaries
  • 6.2 Differential Equations with Unpredictable Solutions
  • 6.3 Discrete Equations with Unpredictable Solutions
  • 6.4 Examples
  • References
  • 7 Strongly Unpredictable Solutions
  • 7.1 Preliminaries
  • 7.2 Main Results
  • 7.3 Examples
  • References
  • 8 Li-Yorke Chaos in Hybrid Systems on a Time Scale
  • 8.1 Introduction
  • 8.2 Preliminaries
  • 8.3 Bounded Solutions
  • 8.4 The Chaotic Dynamics
  • 8.5 An Example
  • 8.6 Notes
  • References
  • 9 Homoclinic and Heteroclinic Motions in Economic Models
  • 9.1 Introduction
  • 9.2 The Model
  • 9.3 Homoclinic and Heteroclinic Motions
  • 9.4 An Example
  • 9.5 Notes
  • References
  • 10 Global Weather and Climate in the Light of El Niño-Southern Oscillation
  • 10.1 Introduction and Preliminaries
  • 10.1.1 Unpredictability of Weather and Deterministic Chaos
  • 10.1.2 Ocean-Atmosphere Interaction and Its Effects on Global Weather
  • 10.1.3 El Niño Chaotic Dynamics
  • 10.1.4 Sea Surface Temperature Advection Equation
  • 10.1.5 Unpredictability and Poincaré Chaos
  • 10.1.6 The Role of Chaos in Global Weather and Climate
  • 10.2 Unpredictable Solution of the Advection Equation
  • 10.2.1 Unpredictability Due to the Forcing Source Term
  • 10.2.2 Unpredictability Due to the Current Velocity
  • 10.3 Chaotic Dynamics of the Global Ocean Parameters
  • 10.3.1 Extension of Chaos in Coupled Advection Equations
  • 10.3.2 Coupling of the Advection Equation with VallisModel
  • 10.3.3 Coupling of Vallis Models
  • 10.4 Ocean-Atmosphere Unpredictability Interaction
  • 10.5 Notes
  • References
  • 11 Fractals: Dynamics in the Geometry
  • 11.1 Introduction
  • 11.2 Fatou-Julia Iteration
  • 11.3 How to Map Fractals
  • 11.4 Dynamics for Julia Sets
  • 11.4.1 Discrete Dynamics
  • 11.4.2 Continuous Dynamics

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