Dynamical Systems

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Main Interest

I´m specially interested in dynamical systems on low dimensions such as endomorphisms on the real line or on the Riemann sphere, diffeomorphisms on dimension 2 or vector fields on dimension ≤ 3. As it is well known, frequently, problems about dynamics in high dimensions depend on lower dimensional phenomena. These interplays between dynamics on high diemnsions and dynamics on low dimensions, which happen for example in the case of the Lorenz and Henon dynamics, is also of my interest.

Some of the questions I'm interested at the moment is part of a big project detailed (in portuguese) in pdf   dvi   ps . Below are the people working in this project.

Albert M. Fisher afsher@ime.usp.br
Andre S. de Carvalho andre@ime.usp.br
Edson de Faria edson@ime.usp.br
Edson Vargas vargas@ime.usp.br
Eduardo Colli colli@ime.usp.br
Fabio A. Tal fabiotal@ime.usp.br
Pedro A. S. Salomão psalomao@ime.usp.br
Salvador A. Zanata sazanata@ime.usp.br

Seminar

The Dynamical Systems Seminar at IME-USP is a forum opened to expositions and discussions of new facts and ideas related to dynamics and it has the participation of researchers from all of the world. The seminar happens during the semester on fridays from 14:00 pm to 16:00 pm at the auditorium Antonio Gilioli. Everybody interested are warmfully invited to participate and proposals of talks can be sent to anyone in the above list or to myself   vargas@ime.usp.br

Students

  1. Cláudia de Oliveira: Dinâmica de funções S-unimodais. Master finished on march/1997.
  2. Yong Su Han: Conjugação quase-simétrica em sistemas dinâmicos unidimensionais. Master finished on january/1999.
  3. Marcio Lima do Nascimento: Dinâmica de recobrimentos do círculo com pontos de inflexão. PhD finished on april/2001.
  4. Liane Bordignon: Decaimento de geometria e mididas invariantes para polinômios cúbicos. PhD finished on march/2003.
  5. Yong Su Han: Polinômios cúbicos Fibonacci, decaimento de geometria e hiperbolicidade induzida. PhD finished on july/2004.

Articles

  1. Vargas, Edson: Fibonacci bimodal maps. Discrete Contin. Dyn. Syst. 22 (2008), no. 3, 807--815. 37E05 (37E15)
  2. Sun, Wenxiang; Vargas, Edson: Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions. Topology Appl. 154 (2007), no. 3, 683--697. (Reviewer: Miaohua Jiang) 37C40 (37A35)
  3. van Strien, Sebastian; Vargas, Edson: Real bounds, ergodicity and negative Schwarzian for multimodal maps. [J. Amer. Math. Soc. 17 (2004), no. 4, 749--782 (electronic); MR2083467]. J. Amer. Math. Soc. 20 (2007), no. 1, 267--268 (electronic). 37E05 (37A25 37D45 37E10)
    Erratum to: "Real bounds, ergodicity and negative Schwarzian for multimodal maps" [J. Amer. Math. Soc. 17 (2004), no. 4, 749--782; MR2083467]. J. Amer. Math. Soc. 20 (2007), no. 1, 267--268 (electronic).
  4. Colli, Eduardo; Vargas, Edson: Non-trivial wandering domains and homoclinic bifurcations. Ergodic Theory Dynam. Systems 21 (2001), no. 6, 1657--1681. (Reviewer: Kazuhiro Sakai) 37G25 (37A99 37D05 37E30)
  5. Sun, Wenxiang; Vargas, Edson: Entropy of flows, revisited. Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), no. 3, 315--333. (Reviewer: Romeo F. Thomas) 37A35 (37B40 37D20)
  6. Swiatek, Grzegorz; Vargas, Edson: Decay of geometry in the cubic family. Ergodic Theory Dynam. Systems 18 (1998), no. 5, 1311--1329. (Reviewer: Henk P. Bruin) 58F23 (30C62)
  7. Vargas, Edson: Measure of minimal sets of polymodal maps. Ergodic Theory Dynam. Systems 16 (1996), no. 1, 159--178. (Reviewer: Antonio Falcó) 58F12 (58F03)
  8. Vargas, Edson: Bifurcation frequency for unimodal maps. Comm. Math. Phys. 141 (1991), no. 3, 633--650. (Reviewer: Frederick R. Marotto) 58F11 (58F03)
  9. Vargas, Edson: Markov partition in nonhyperbolic interval dynamics. Comm. Math. Phys. 138 (1991), no. 3, 521--535. (Reviewer: Sebastian van Strien) 58F11 (58F15)
  10. de Faria, Edson; de Melo, Welington; Salomão, Pedro A. S.; Vargas, Edson: Full families of multimodal maps on the circle. Pré-print.
  11. Colli, E.; Nascimento, M. L.; Vargas, E.: Decay of geometry for Fibonacci critical covering of the circle. Pré-print.
  12. Vargas, E.: Decay of geometry for cubic Fibonacci polynomials. Pré-print

Talks

  1. Full families of multimodal maps on the circle. ppt  
  2. Koebe principles and negative Schwarzian for multimodal maps.   pdf  
  3. Non-existence of wandering intervals for multimodal maps.   pdf  
  4. Limites a priori reais, ergodicidade e derivada de Schwarz.   pdf  
  5. Metric aspects of the dynamics of covering maps of the circle.   pdf  

English CV

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