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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
8.
Fractal Geometry
8.1.
Introduction to Fractals
8.1.1.
Definition and Characteristics
8.1.2.
Self-Similarity
8.1.3.
Scale Invariance
8.1.4.
Fractal vs. Euclidean Geometry
8.2.
Fractal Dimension
8.2.1.
Hausdorff Dimension
8.2.2.
Box-Counting Dimension
8.2.3.
Correlation Dimension
8.2.4.
Information Dimension
8.2.5.
Generalized Dimensions
8.3.
Classical Fractals
8.3.1.
Cantor Set
8.3.1.1.
Construction
8.3.1.2.
Measure and Dimension
8.3.2.
Sierpinski Triangle
8.3.3.
Koch Snowflake
8.3.4.
Dragon Curve
8.3.5.
Menger Sponge
8.4.
Random Fractals
8.4.1.
Brownian Motion
8.4.2.
Fractional Brownian Motion
8.4.3.
Percolation Clusters
8.5.
Fractals in Dynamical Systems
8.5.1.
Julia Sets
8.5.1.1.
Definition and Construction
8.5.1.2.
Filled Julia Sets
8.5.1.3.
Connection to Dynamics
8.5.2.
Mandelbrot Set
8.5.2.1.
Definition in Parameter Space
8.5.2.2.
Relationship to Julia Sets
8.5.2.3.
Self-Similarity and Universality
8.5.3.
Fractal Basin Boundaries
8.5.4.
Strange Attractors as Fractals
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9. Hamiltonian Dynamics and Conservative Systems