Non-integrable Flat Dynamical Systems
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A01=Jozsef Beck
A01=William Chen
A01=Yuxuan Yang
Anti-Uniformity
Author_Jozsef Beck
Author_William Chen
Author_Yuxuan Yang
Billiard
Category=PBM
Category=PBV
Density
Dissipative
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Ergodic Theory
Flat Systems
Geodesic
Optimal
Region
Superdense
Superuniform
Surface
Time Quantitative
Translation Surface
Uniformity
Product details
- ISBN 9789819803156
- Publication Date: 22 Sep 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book provides a systematic introduction and treatment of non-integrable flat systems. More precisely, it develops analogues of the well-known Kronecker-Weyl equidistribution theorem for various non-integrable flat systems. The distribution properties of half-infinite geodesics in non-integrable flat dynamical systems are investigated, with particular emphasis on density and uniformity on various flat surfaces, as well as generalizations to higher dimensions and related problems.The approach to addressing some of these uniformity questions combines traditional ergodic theory methods, such as the Birkhoff ergodic theorem, with tools from number theory and new ideas outside the field of ergodic theory. Several non-trivial results on 3-dimensional flat systems are included, expanding upon the extensive literature on 2-dimensional non-integrable flat dynamical systems, which often focuses on plane-specific methods that do not readily adapt to 3-dimensional systems. New approaches are developed to address these challenges.A systematic study of a class of dissipative systems is also presented, where the flow is neither time-reversible nor measure-preserving. The overwhelming majority of the material in this book represents previously unpublished research.
