Classical and Dynamical Markov and Lagrange Spectra PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Classical and Dynamical Markov and Lagrange Spectra PDF full book. Access full book title Classical and Dynamical Markov and Lagrange Spectra by Davi Lima. Download full books in PDF and EPUB format.
Author: Davi Lima
Publisher:
ISBN: 9789811225284
Category :
Languages : en
Pages : 228
Get Book Here
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: 9789811225284
Category :
Languages : en
Pages : 228
Get Book Here
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 :
Get Book Here
Book Description
Author: Davi Dos Santos Lima
Publisher: World Scientific
ISBN: 9811225303
Category : Mathematics
Languages : en
Pages : 228
Get Book Here
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:
Author: Henk Bruin
Publisher: American Mathematical Society
ISBN: 1470472198
Category : Mathematics
Languages : en
Pages : 481
Get Book Here
Book Description
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Author: Thomas W. Cusick
Publisher: American Mathematical Soc.
ISBN: 0821815318
Category : Mathematics
Languages : en
Pages : 109
Get Book Here
Book Description
This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 1288
Get Book Here
Book Description
Author: Mark Agranovsky
Publisher: Birkhäuser
ISBN: 3319701541
Category : Mathematics
Languages : en
Pages : 373
Get Book Here
Book Description
This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.
Author: Garnett Williams
Publisher: CRC Press
ISBN: 1482295415
Category : Mathematics
Languages : en
Pages : 518
Get Book Here
Book Description
This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.
Author: Jacob Palis Júnior
Publisher: Cambridge University Press
ISBN: 9780521475723
Category : Mathematics
Languages : en
Pages : 248
Get Book Here
Book Description
A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
Author: Anatole Katok
Publisher: Cambridge University Press
ISBN: 9780521575577
Category : Mathematics
Languages : en
Pages : 828
Get Book Here
Book Description
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
