Strong Uniformity and Large Dynamical Systems

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, Mathematical Physics
Cover of the book Strong Uniformity and Large Dynamical Systems by Jozsef Beck, World Scientific Publishing Company
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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
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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:

Readership: Researchers in dynamical systems and ergodic theory and statistical physics.
Key Features:

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