Non-integrable Dynamics: Time-quantitative Results
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€179.80
A01=Jozsef Beck
A01=William Chen
A01=Yuxuan Yang
Ancestor
Author_Jozsef Beck
Author_William Chen
Author_Yuxuan Yang
Billiard
Category=PB
Category=PBV
Category=PHU
Density
eq_bestseller
eq_isMigrated=1
eq_nobargain
eq_non-fiction
eq_science
Geodesic
Irregularity Exponent
Region
Shortline
Superdense
Superuniform
Surface
Time-Quantitative
Translation Surface
Uniformity
Product details
- ISBN 9789811273858
- Publication Date: 18 Sep 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
