Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects

Carlos Matheus Silva Santos (Cnrs, France and Univ Paris 13, France;), Sergio Augusto Romana Ibarra (Univ Federal Do Rio De Janeiro,brazil), Carlos Gustavo Moreira (Impa,brazil), Davi Dos Santos Lima (Univ Federal De Alagoas, Brazil)

ISBN 10: 9811225281 / ISBN 13: 9789811225284

Published by World Scientific Publishing Co Pte Ltd, SG, 2020

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: Seller Inventory # LU-9789811225284

Synopsis:

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

Readership: Graduate students and researchers in Number Theory and Dynamical Systems.

From the Back Cover: 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 Teichmller dynamics

Bibliographic Details

Title: Classical And Dynamical Markov And Lagrange ...
Publisher: World Scientific Publishing Co Pte Ltd, SG
Publication Date: 2020
Binding: Hardback
Condition: New