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 ...
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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.
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New. Intended for college/higher education audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Non-integrable Dynamics: Time-quantitative Results to cart. $176.18, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2023 by World Scientific Publishing Co Pte Ltd.
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Fine. Intended for college/higher education audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
