CLASSICAL AND DYNAMICAL MARKOV AND LAGRANGE SPECTRA: DYNAMICAL, FRACTAL AND ARITHMETIC ASPECTS. Questo articolo non è disponibile.CLASSICAL AND DYNAMICAL MARKOV AND LAGRANGE SPECTRA: DYNAMICAL, FRACTAL AND ARITHMETIC ASPECTS

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

Davi Lima is a young PhD in Mathematics who is professor at Universidade Federal de Alagoas (UFAL) and does research in Dynamical Systems and Number Theory. He has fun giving classes on Math Olympiads for young people from Alagoas and saying that Palmeiras is the best football team in the world.

Carlos Matheus is directeur de recherche (CNRS) at Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique, France. Among his current collective responsibilities, one finds that he serves as an editor of Journal of the European Mathematical Society and Journal of Modern Dynamics, a survey editor of Ergodic Theory and Dynamical Systems, and the curator of Yoccoz's mathematical archives.

Carlos Gustavo Moreira is a Full Professor of IMPA, Rio de Janeiro, Brazil and Invited Professor of Nankai University, in Nanjing. Concluded his PhD in 1993 under the supervision of Jacob Palis. Has more than 70 scientific publications. He was awarded with a Gold Medal in the 31st IMO, in Beijing in 1990, the UMALCA Prize in 2009, the TWAS Prize in Mathematics in 2010. He is Fellow of the Brazilian Academy of Sciences since 2008 and of TWAS since 2012. He gave an invited lecture in the Dynamical Systems session of the ICM 2014, in Seoul, and a Plenary Lecture in the ICM 2018, in Rio de Janeiro.

Sergio Romaña is professor at Universidade Federal do Rio de Janeiro and does research in Dynamical Systems, Ergodic Theory and on the interplay between Dynamical Systems and Differential Geometry.