Strong Uniformity and Large Dynamical Systems
Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, Mathematical Physics
| Author: | Jozsef Beck | ISBN: | 9789814740760 |
| Publisher: | World Scientific Publishing Company | Publication: | July 7, 2017 |
| Imprint: | WSPC | Language: | English |
| Author: | Jozsef Beck |
| ISBN: | 9789814740760 |
| Publisher: | World Scientific Publishing Company |
| Publication: | July 7, 2017 |
| Imprint: | WSPC |
| Language: | English |
It is the first book about a new aspect of Uniform distribution, called Strong Uniformity. Besides developing the theory of Strong Uniformity, the book also includes novel applications in the underdeveloped field of Large Dynamical Systems.
Contents:
-
From Uniform Distribution to the Time-Evolution of Large Off-Equilibrium Systems:
- Traditional Uniform Distribution and Weyl's Criterion
- Strong Uniformity
- High-Dimensional Configuration Space of Large Systems and Unrealistic Time Scale
- Dimension-Free Strong Uniformity on a Realistic Time Scale
- Rapid Approach and Long-Term Stability of Square-Root Equilibrium
- Non-ergodic Time-flow: Closed Orbit Spherical Systems
- Closed Orbit Polar Systems
- Snapshot Randomness (I): Poisson
- Proofs of Theorems 4.2 and 4.3
-
General Models:
- General Model: Unique Ergodicity via Typical Rotations
- Asymptotic Time-Lapse Randomness
- Short-Term Time-Lapse Randomness: Multiple Mixedupness (I)
- Extensions of Theorem 4.2 beyond the Gaussian Case
- Extensions of Theorem 4.2 to Nonlinear Curves on the Plane
-
More Applications of Theorem 4.2:
- Snapshot Randomness (II): Central Limit Theorem
- Snapshot Randomness (III) Case of Closed Orbits
- Time-Lapse Randomness vs Snapshot Randomness (I): A Fundamental Difference
- Time-Lapse Randomness vs Snapshot Randomness (II): A Fundamental Difference
- CLT Time-Lapse Randomness: Upper Bound
-
More Results about Randomness and Stability in Equilibrium:
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (I)
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (II)
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (III)
- On the Square-Root Logarithmic Threshold in the Gaussian Case
- Beyond the Applications of Theorem 4.2
- The Case of Singular Underlying Measure
-
More Proofs:
- Proof of Theorem 4.1
- Starting the Proofs of Theorems 13.1–13.4
- Completing the Proof of Lemma 27.2
- Finishing the Proofs of Theorems 13.1–13.4
- Starting the Proof of Theorem 14.1
- Finishing the Proof of Theorem 14.1
- Proof of Theorem 14.2
- Multiple Mixedupness (II): Proof of Lemma 12.2
- Multiple Mixedupness (III): Proof of Theorem 12.2
Readership: Researchers in dynamical systems and ergodic theory and statistical physics.
Key Features:
- It is the first book about the subject, so it is unique
- The book is basically my contribution to the field
It is the first book about a new aspect of Uniform distribution, called Strong Uniformity. Besides developing the theory of Strong Uniformity, the book also includes novel applications in the underdeveloped field of Large Dynamical Systems.
Contents:
-
From Uniform Distribution to the Time-Evolution of Large Off-Equilibrium Systems:
- Traditional Uniform Distribution and Weyl's Criterion
- Strong Uniformity
- High-Dimensional Configuration Space of Large Systems and Unrealistic Time Scale
- Dimension-Free Strong Uniformity on a Realistic Time Scale
- Rapid Approach and Long-Term Stability of Square-Root Equilibrium
- Non-ergodic Time-flow: Closed Orbit Spherical Systems
- Closed Orbit Polar Systems
- Snapshot Randomness (I): Poisson
- Proofs of Theorems 4.2 and 4.3
-
General Models:
- General Model: Unique Ergodicity via Typical Rotations
- Asymptotic Time-Lapse Randomness
- Short-Term Time-Lapse Randomness: Multiple Mixedupness (I)
- Extensions of Theorem 4.2 beyond the Gaussian Case
- Extensions of Theorem 4.2 to Nonlinear Curves on the Plane
-
More Applications of Theorem 4.2:
- Snapshot Randomness (II): Central Limit Theorem
- Snapshot Randomness (III) Case of Closed Orbits
- Time-Lapse Randomness vs Snapshot Randomness (I): A Fundamental Difference
- Time-Lapse Randomness vs Snapshot Randomness (II): A Fundamental Difference
- CLT Time-Lapse Randomness: Upper Bound
-
More Results about Randomness and Stability in Equilibrium:
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (I)
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (II)
- Simultaneous Square-Root Equilibrium Relative to Nice Sets (III)
- On the Square-Root Logarithmic Threshold in the Gaussian Case
- Beyond the Applications of Theorem 4.2
- The Case of Singular Underlying Measure
-
More Proofs:
- Proof of Theorem 4.1
- Starting the Proofs of Theorems 13.1–13.4
- Completing the Proof of Lemma 27.2
- Finishing the Proofs of Theorems 13.1–13.4
- Starting the Proof of Theorem 14.1
- Finishing the Proof of Theorem 14.1
- Proof of Theorem 14.2
- Multiple Mixedupness (II): Proof of Lemma 12.2
- Multiple Mixedupness (III): Proof of Theorem 12.2
Readership: Researchers in dynamical systems and ergodic theory and statistical physics.
Key Features:
- It is the first book about the subject, so it is unique
- The book is basically my contribution to the field
