Spaces of Dynamical Systems 2nd Edition by Sergei Pilyugin ISBN 3110653990 9783110653991

Spaces of Dynamical Systems 2nd Edition by Sergei Yu. Pilyugin – Ebook PDF Instant Download/Delivery: 3110653990, 978-3110653991
Full download Spaces of Dynamical Systems 2nd Edition after payment

 

Product details:

ISBN 10:      3110653990
ISBN 13: 978-3110653991
Author:      Sergei Yu. Pilyugin

 

Spaces of Dynamical Systems (2nd Edition) by Sergei Pilyugin is a mathematical text that delves into the study of dynamical systems, particularly focusing on the properties and structure of the spaces in which these systems evolve. The book is designed for graduate students and researchers with a background in mathematics, particularly in areas such as topology, differential equations, and dynamical systems theory.

Key Features and Description:

1. Comprehensive Overview of Dynamical Systems: This book offers a systematic and in-depth exploration of the theory of dynamical systems, including continuous and discrete systems. It covers both theoretical aspects and practical approaches to analyzing the behavior of complex systems over time.

2. Spaces of Dynamical Systems: The second edition places a special emphasis on the spaces in which dynamical systems operate. It explores the topology and geometry of these spaces, providing tools for understanding their structure and the dynamics within them.

3. Mathematical Framework: The text integrates concepts from various mathematical disciplines including topology, algebra, and analysis, making it an ideal resource for advanced students and researchers looking to develop a deep understanding of dynamical systems theory. It introduces various types of dynamical systems such as flows, maps, and systems with discrete time, and relates them to topological and geometric methods.

4. Applications and Examples: The book provides numerous examples and applications of dynamical systems in real-world contexts, such as in physics, biology, economics, and engineering. These examples illustrate how abstract mathematical concepts can be used to understand and model dynamic processes in nature and human-made systems.

5. Updates in the Second Edition: The second edition features new material and updates, reflecting the latest developments in the field of dynamical systems. It offers revised proofs, new examples, and expanded coverage of current research trends.

6. Mathematical Rigor: The book is known for its precise and rigorous approach, making it suitable for those pursuing advanced study or research in dynamical systems. It assumes a solid foundation in mathematics, particularly in analysis and topology.

Spaces of Dynamical Systems 2nd Table of contents:

 

1. Dynamical Systems

1. Main Definitions
2. Embedding of a Discrete Dynamical System into a Flow
3. Local Poincaré Diffeomorphism
4. Time-Periodic Systems of Differential Equations
5. Action of a Group

---

2. Topologies on Spaces of Dynamical Systems

1. C0-Topology
2. C1-Topology
3. Metrics on the Space of Systems of Differential Equations
4. Generic Properties
5. Immersions and Embeddings

---

3. Equivalence Relations

1. Topological Conjugacy
2. Topological Equivalence of Flows
3. Nonwandering Set
4. Local Equivalence

---

4. Hyperbolic Fixed Point

1. Hyperbolic Linear Mapping
2. The Grobman–Hartman Theorem
3. Neighborhood of a Hyperbolic Fixed Point
4. The Stable Manifold Theorem
5. Hyperbolic Periodic Point

---

5. Hyperbolic Rest Point and Hyperbolic Closed Trajectory

1. Hyperbolic Rest Point
2. Hyperbolic Closed Trajectory

---

6. Transversality

1. Transversality of Mappings and Submanifolds
2. Transversality Condition
3. Palis Lemma
4. Transversality and Hyperbolicity for One-Dimensional Mappings

---

7. Hyperbolic Sets

1. Definition of a Hyperbolic Set
2. Examples of Hyperbolic Sets
3. Basic Properties of Hyperbolic Sets
4. Stable Manifold Theorem
5. Axiom A
6. Hyperbolic Sets of Flows

---

8. Anosov Diffeomorphisms

---

9. Smale’s Horseshoe and Chaos

1. Smale’s Horseshoe
2. Chaotic Sets
3. Homoclinic Points

---

10. Closing Lemma

---

11. C0-Generic Properties of Dynamical Systems

1. Hausdorff Metric
2. Semicontinuous Mappings
3. Tolerance Stability and Takens’ Theory
4. Attractors of Dynamical Systems

---

12. Shadowing of Pseudotrajectories in Dynamical Systems

1. Definitions and Results
2. Proof of Theorem 12.1
3. Proof of Theorem 12.2
4. Proof of Theorem 12.3

---

13. Invariant Measures

1. Main Definitions
2. Construction of Invariant Measures
3. Krylov–Bogolyubov Theorem
4. Ergodic Theorems
5. Poincaré Recurrence and Hamiltonian Systems
6. Ergodic Closing Lemma

People also search for Spaces of Dynamical Systems 2nd:

spatial dynamics definition
space systems design
topological invariants of dynamical systems and spaces of holomorphic maps
dynamical systems syllabus
applications of dynamical systems

Tags:

Sergei Pilyugin,Spaces,Dynamical,Systems 2nd