Marcelo Viana - Selected Works

ISBN-13: 9783031019746 / Angielski / Miękka / 2023

Marcelo Viana

Opis

Dynamical systems and the twin field ergodic theory have their roots in the qualitative theory of differential equations, developed by the great mathematician Henri Poincaré, and in the kinetic theory of gases built in mathematical terms by physicists James Clerk Maxwell and Ludwig Boltzmann. Together, they aim to model, explain and predict the behavior of natural and artificial phenomena which evolve in time.  For more than three decades, Marcelo Viana has been making several outstanding contributions to this area of mathematics. This volume contains a selection of his research papers, covering a wide range of topics: rigorous theory of strange attractors, physical measures, bifurcation theory, homoclinic phenomena, fractal dimensions, partial hyperbolicity, thermodynamic formalism, non-uniform hyperbolicity, interval exchange maps Teichmüller flows, and the modern theory of Lyapunov exponents.Marcelo Viana, a world leader in this field, has been the object of several academic distinctions, such as the inaugural Ramanujan prize of the International Centre for Theoretical Physics, and the Louis D. Scientific Grand Prix of the Institut de France. He is also recognized for his broad contribution to the mathematical community, in his country and region as well as in the international arena.

Spis treści

Moduli of continuity for the Lyapunov exponents of random GL(2)-cocycles: El Hadji Yaya Tall and Marcelo Viana.- Continuity of Lyapunov exponents in the C 0 topology: Marcelo Viana and Jiagang Yang.- Continuity of Lyapunov exponents for random two-dimensional matrices: Carlos Bocker-Neto and Marcelo Viana.- Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows: Artur Avila, Marcelo Viana and Amie Wilkinson.- Holonomy invariance: rough regularity and applications to Lyapunov exponents: Artur Avila, Jimmy Santamaria and Marcelo Viana.- Extremal Lyapunov exponents: an invariance principle and applications: Artur Avila and Marcelo Viana.- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents: Marcelo Viana.- Simplicity of Lyapunov spectra: proof of the Zorich–Kontsevich conjecture: Artur Avila and Marcelo Viana.- The Lyapunov exponents of generic volume-preserving and symplectic maps: Jairo Bochi and Marcelo Viana.- xv Contents Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices [Genericity of non-zero Lyapunov exponents for deterministic products of matrices]: Christian Bonatti, Xavier Gómez-Mont and Marcelo Viana.- Solution of the basin problem for Hénon-like attractors: Michael Benedicks and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly contracting: Christian Bonatti and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly expanding: José F. Alves, Christian Bonatti and Marcelo Viana.- Multidimensional nonhyperbolic attractors: Marcelo Viana.- Strange attractors in saddle-node cycles: prevalence and globality: L.J. Diaz, J. Rocha and M. Viana.- High dimension diffeomorphisms displaying infinitely many periodic attractors: J. Palis and M. Viana.- Abundance of strange attractors: Leonardo Mora and Marcelo Viana.- List of Publications of Marcelo Viana.- List of Ph.D. Students of Marcelo Viana at IMPA.- Credits.

O autorze

Marcelo Viana is a professor of mathematics and the current director of the Instituto de Matemática Pura e Aplicada in Rio de Janeiro. A specialist in dynamical systems and ergodic theory, he published about sixty research papers and supervised over forty Ph.D. students. He was the president of the Brazilian Mathematical Society and a vice-president of the International Mathematical Union. He is a member of four academies of sciences and received several academic distinctions, such as the inaugural Ramanujan prize of the International Centre for Theoretical Physics and the Louis D. Scientific Grand Prix, of the Institut de France. He organized the 2018 International Congress of Mathematicians, and is a driving force in the Mathematical Council of the Americas, the continental network that he helped create in 2012.  He writes a weekly column about science in Folha de São Paulo, Brazil's prominent newspaper.