Dynamics with Chaos and Fractals. 1st ed. 2020
- 種類:
- 電子ブック
- 責任表示:
- by Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
- 出版情報:
- Cham : Springer International Publishing : Imprint: Springer, 2020
- 著者名:
- シリーズ名:
- Nonlinear Systems and Complexity ; 29
- ISBN:
- 9783030358549 [3030358542]
- 注記:
- Chapter 1. Introduction -- Chapter 2. The Unpredictable Point and Poincare Chaos -- Chapter 3. Unpredictability in Bebutov Dynamics -- Chapter 4. Non-linear Unpredictable Perturbations -- Chapter 5. Unpredictability in Topological Dynamics -- Chapter 6. Unpredictable Solutions of Hyperbolic Linear Equations -- Chapter 7. Strongly Unpredictable Solutions -- Chapter 8. Li-Yorke Chaos in Hybrid Systems on a Time Scale -- Chapter 9. Homoclinic and Heteroclinic Motions in Economic Models -- Chapter 10. Global Weather and Climate in the light of El Nino-Southern Oscillation -- Chapter 11. Fractals: Dynamics in the Geometry -- Chapter 12. Abstract Similarity, Fractals and Chaos.
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 point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested. The Book Stands as the first book presenting the - ローカル注記:
- 学内専用E-BOOKS (local access only)
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