Scaling laws in dynamical systems

Scaling laws in dynamical systems / Edson Denis Leonel

This book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by...

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Bibliographic Details
Main Author: Leonel, Edson Denis (Author)
Format: eBook
Language:English
Published: Singapore : Springer, 2021.
Series:Nonlinear physical science.
Subjects:
Scaling laws (Statistical physics)
Nonlinear mechanics.
Nonlinear mechanics
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Acknowledgements
  • Contents
  • List of Figures
  • List of Tables
  • 1 Introduction
  • 1.1 Initial Concepts
  • 1.2 Summary
  • 2 One-Dimensional Mappings
  • 2.1 Introduction
  • 2.2 The Concept of Stability
  • 2.2.1 Asymptotically Stable Fixed Point
  • 2.2.2 Neutral Stability
  • 2.2.3 Unstable Fixed Point
  • 2.3 Fixed Points to the Logistic Map
  • 2.4 Bifurcations
  • 2.4.1 Transcritical Bifurcation
  • 2.4.2 Period Doubling Bifurcation
  • 2.4.3 Tangent Bifurcation
  • 2.5 Summary
  • 2.6 Exercises
  • 3 Some Dynamical Properties for the Logistic Map
  • 5.1 Linear Mappings
  • 5.2 Nonlinear Mappings
  • 5.3 Applications of Two Dimensional Mappings
  • 5.3.1 Hénon Map
  • 5.3.2 Lyapunov Exponents
  • 5.3.3 Ikeda Map
  • 5.4 Summary
  • 5.5 Exercises
  • 6 A Fermi Accelerator Model
  • 6.1 Fermi-Ulam Model
  • 6.1.1 Jacobian Matrix for the Indirect Collisions
  • 6.1.2 Jacobian Matrix for the Direct Collisions
  • 6.1.3 Fixed Points
  • 6.1.4 Phase Space
  • 6.1.5 Phase Space Measure Preservation
  • 6.2 A Simplified Version of the Fermi-Ulam Model
  • 6.3 Scaling Properties for the Chaotic Sea
  • 6.4 Localization of the First Invariant Spanning Curve

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