Classical and Dynamical Markov and Lagrange Spectra

Released on by Davi Lima
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  • Classical and Dynamical Markov and Lagrange Spectra Book Detail

  • Author : Davi Lima
  • Release Date : 2020-09-14
  • Publisher :
  • Genre :
  • Pages : 228
  • ISBN 13 : 9789811225284
  • File Size : 24,24 MB
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Classical and Dynamical Markov and Lagrange Spectra by Davi Lima PDF Summary

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

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The Markoff and Lagrange Spectra

The Markoff and Lagrange Spectra

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This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Mark