Author: Yuan-Chwen You
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 102
Book Description
Role of the Rationals in the Markov and Lagrange Spectra
Author: Yuan-Chwen You
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 102
Book Description
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 102
Book Description
Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects
Author: Davi Dos Santos Lima
Publisher: World Scientific
ISBN: 9811225303
Category : Mathematics
Languages : en
Pages : 228
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:
Publisher: World Scientific
ISBN: 9811225303
Category : Mathematics
Languages : en
Pages : 228
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:
The Markoff and Lagrange Spectra
Author: Thomas W. Cusick
Publisher: American Mathematical Soc.
ISBN: 9780821874851
Category : Lagrange spectrum
Languages : en
Pages : 150
Book Description
Publisher: American Mathematical Soc.
ISBN: 9780821874851
Category : Lagrange spectrum
Languages : en
Pages : 150
Book Description
Markov's Theorem and 100 Years of the Uniqueness Conjecture
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3319008889
Category : Mathematics
Languages : en
Pages : 257
Book Description
This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Publisher: Springer Science & Business Media
ISBN: 3319008889
Category : Mathematics
Languages : en
Pages : 257
Book Description
This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Geometric Properties of the Markov and Lagrange Spectra
Author: Carlos Gustavo Moreira
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Dissertation Abstracts International
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 798
Book Description
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 798
Book Description
The Markoff and Lagrange Spectra
Author: Thomas W. Cusick
Publisher: American Mathematical Soc.
ISBN: 0821815318
Category : Mathematics
Languages : en
Pages : 109
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.
Publisher: American Mathematical Soc.
ISBN: 0821815318
Category : Mathematics
Languages : en
Pages : 109
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.
Catalog of Copyright Entries. Third Series
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1666
Book Description
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1666
Book Description
Comprehensive Dissertation Index
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 896
Book Description
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 896
Book Description
National Union Catalog
Author:
Publisher:
ISBN:
Category : Union catalogs
Languages : en
Pages : 816
Book Description
Publisher:
ISBN:
Category : Union catalogs
Languages : en
Pages : 816
Book Description