Geometric Properties of the Markov and Lagrange Spectra PDF Download
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Author: Carlos Gustavo Moreira
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Carlos Gustavo Moreira
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Davi Lima
Publisher:
ISBN: 9789811225284
Category :
Languages : en
Pages : 228
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Book Description
The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry. Besides presenting many classical results, the book includes several topics of recent research on the subject, connecting several fields of Mathematics -- Number Theory, Dynamical Systems and Fractal Geometry. It includes topics as: Classical results on the Markov and Lagrange spectra: the Markov theorem on the lower spectra The fractal geometry of the complement of the Lagrange spectrum in the Markov spectrum Continuity of Hausdorff dimension of the spectra intersected with half-lines: the classical spectra and dynamical generalizations Intervals in the classical spectra and dynamical generalizations The beginning of the spectra: discrete initial part and first accumulation points (in the classical and dynamical cases) Markov and Lagrange spectra for Teichmüller dynamics
Author: Davi Lima
Publisher:
ISBN: 9789811225291
Category : Electronic books
Languages : en
Pages :
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Author: Sébastien Ferenczi
Publisher: Springer
ISBN: 3319749080
Category : Mathematics
Languages : en
Pages : 434
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Book Description
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Author: Sirakov Boyan
Publisher: World Scientific
ISBN: 9813272899
Category : Mathematics
Languages : en
Pages : 5396
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Book Description
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author: Thomas W. Cusick
Publisher: American Mathematical Soc.
ISBN: 9780821874851
Category : Lagrange spectrum
Languages : en
Pages : 150
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Book Description
Author: Bogdan Grechuk
Publisher: Springer
ISBN: 303019096X
Category : Mathematics
Languages : en
Pages : 446
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Book Description
This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.
Author: Luca Dal Negro
Publisher:
ISBN: 1009178180
Category : Science
Languages : en
Pages : 714
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Book Description
This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics.
Author: Yuan-Chwen You
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 102
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Book Description
Author: Christian Bonatti
Publisher: Springer Science & Business Media
ISBN: 9783540220664
Category : Mathematics
Languages : en
Pages : 408
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Book Description
The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically. Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for "most" dynamical systems, recovering as much as possible of the conclusions of the uniformly hyperbolic case, in great generality. This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed at researchers, both young and senior, willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.
