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Physics
Applied and Interdisciplinary Physics
Nonlinear Dynamics and Chaos
1. Introduction to Dynamical Systems
2. One-Dimensional Flows
3. Two-Dimensional Flows
4. Higher-Dimensional Systems
5. Introduction to Chaos in Continuous Systems
6. Discrete Dynamical Systems and Maps
7. Universality and Scaling
8. Fractal Geometry
9. Hamiltonian Dynamics and Conservative Systems
10. Synchronization Phenomena
11. Control of Chaos
12. Spatiotemporal Dynamics
13. Time Series Analysis
14. Applications in Physical Sciences
15. Applications in Life Sciences
16. Applications in Chemistry
17. Applications in Engineering
18. Applications in Economics and Social Sciences
19. Computational Methods
6.
Discrete Dynamical Systems and Maps
6.1.
One-Dimensional Maps
6.1.1.
Basic Concepts
6.1.1.1.
Iteration and Orbits
6.1.1.2.
Fixed Points and Periodic Points
6.1.1.3.
Graphical Analysis (Cobweb Plots)
6.1.2.
The Logistic Map
6.1.2.1.
Mathematical Formulation
6.1.2.2.
Parameter Dependence
6.1.2.3.
Fixed Point Analysis
6.1.2.4.
Period-Doubling Cascade
6.1.2.5.
Chaotic Regime
6.1.2.6.
Symbolic Dynamics
6.1.3.
Other Important Maps
6.1.3.1.
Tent Map
6.1.3.2.
Shift Map
6.1.3.3.
Circle Map
6.1.3.4.
Quadratic Family
6.2.
Stability and Bifurcations in Maps
6.2.1.
Linear Stability Analysis
6.2.2.
Period-Doubling Bifurcations
6.2.3.
Tangent Bifurcations
6.2.4.
Flip Bifurcations
6.3.
Routes to Chaos
6.3.1.
Period-Doubling Route
6.3.1.1.
Feigenbaum Scenario
6.3.1.2.
Universal Constants
6.3.2.
Intermittency
6.3.2.1.
Type I Intermittency
6.3.2.2.
Type II Intermittency
6.3.2.3.
Type III Intermittency
6.3.3.
Quasiperiodic Route
6.3.3.1.
Circle Maps
6.3.3.2.
Mode Locking
6.3.3.3.
Arnold Tongues
6.4.
Two-Dimensional Maps
6.4.1.
The Hénon Map
6.4.1.1.
Mathematical Definition
6.4.1.2.
Parameter Space
6.4.1.3.
Chaotic Attractors
6.4.2.
Standard Map
6.4.2.1.
Physical Context
6.4.2.2.
KAM Theory
6.4.2.3.
Chaos and Integrability
6.4.3.
Baker's Map
6.4.4.
Horseshoe Map
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7. Universality and Scaling