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Kniha Non-Integrable Dynamics: Time-Quantitative Results William Chen

Non-Integrable Dynamics: Time-Quantitative Results

Autor: William Chen, Yuxuan Yang
Jazyk: Angličtina
Vazba: Pevná
Vydavatel: WORLD SCIENTIFIC PUB CO INC
Dostupnost: Skladem u dodavatele
Odesíláme za 9-15 dnů
3 713 Kč
The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic...

Informace o knize

Autor
William Chen, Yuxuan Yang
Jazyk
Angličtina
Vazba
Kniha - Pevná
Vydáno
2023
Stránek
400
EAN
9789811273858
ISBN
9811273855
Enbook ID
43094455
Vydavatel
WORLD SCIENTIFIC PUB CO INC
Hmotnost
834

Kompletní popis

The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.


The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.


Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.

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