Ricardo Mañé - Selected Papers

ISBN-13: 9783319416632 / Angielski / Twarda / 2017 / 646 str.

Ricardo Mane; Maria Jose Pacifico

Opis

This volume presents selected papers by the brilliant Uruguayan mathematician Ricardo Mane, known for his outstanding contributions to dynamical systems and ergodic theory. He was a student of Jacob Palis at IMPA and pursued his whole scientific career at IMPA. Mane was invited to speak twice in the section of Ordinary Differential Equations and Dynamical Systems, at the International Congress of Mathematics held in Warsaw in 1983 and in Zurich in 1994. He was also a speaker at the Colloquium organized by the Societe Mathematique de France, celebrating R. Thom s 65 anniversary.
In 1994, he became a member of the Brazilian Academy of Sciences and was awarded the Third World Academy of Sciences Prize for Mathematics."

Spis treści

1. Persistent manifolds are normally hyperbolic.- 2. Invariant sets of Anosov’s diffeomorphisms.- 3. An ergodic closing lemma.- 4. On the entropy of the geodesic flow in manifolds without conjugate points (with A. Freire).- 5. An invariant measure for rational maps (with A. Freire and A. Lopes).- 6. On the uniqueness of the maximizing measure for rational maps.- 7. On the dynamics of rational maps (with P.Sad and D. Sullivan).- 8. Lyapounov exponents and stable manifolds for compact transformations.- 9a. Hyperbolicity, sinks and measure in one-dimensional dynamics.- 9b. Erratum - Hyperbolicity, sinks and measure in one-dimensional dynamics.- 10. On the instability of Herman rings.- 11. On a theorem of Klingenberg.- 12. The Hausdorff dimension of invariant probabilities of rational maps.- 13. On the creation of homoclinic points.- 14. A proof of the C 1 stability conjecture.- 15. The explosion of singular cycles (with R. Bamón, R. Labarca, and M.J. Pacifico).- 16. On a theorem of Fatou.- 17. Ergodic variational methods: new techniques and new problems.- 18. On the topological entropy of geodesic flows.- 19. Lagrangian flows: the dynamics of globally minimizing orbits. II (by G. Contreras, J. Delgado, and R. Iturriaga).-  20. Oseledec’s theorem from the generic viewpoint.- 21. Contributions to the stability conjecture.- 22. A proof of Pesin's formula.- 23. On the Bernoulli property for rational maps.- 24. On the minimizing measures of Lagrangian dynamical systems.- 25. The Lyapunov exponents of generic area preserving diffeomorphisms.- 26. The Dynamics of Inner Functions (with Claus I. Doering).

O autorze

Ricardo Mañé was a brilliant Uruguayan mathematician, known for his outstanding contributions to dynamical systems and ergodic theory. He was a student of Jacob Palis at IMPA and pursued his whole  scientific career at IMPA.

Mañé was invited to speak twice in the section of Ordinary Differential Equations and Dynamical Systems, at the International Congress of Mathematics held in Warsaw in 1983 and in Zurich in 1994. He was also a speaker at the Colloquium organized by the Societé Mathématique de France, celebrating R. Thom’s 65 anniversary.

In 1994, he became a member of the Brazilian Academy of Sciences and was awarded the Third World Academy of Sciences Prize for Mathematics.