Programa de Verão 2016

Para o Programa de Verão de 2016, o Instituto de Matemática da UFRJ está oferecendo os seguintes cursos:

Autores: Dr Alfonso Artigue (Universidad de la Repu´blica, Uruguay) & Dr. José Vieitez (Universidad de la Repu´blica, Uruguay)
Ementa: Basic results: uniform expansiveness, Lyapunov functions, topology of stable sets: case of a manifold. Classification of expansive homeomorphisms on surfaces. Some aspects on greater dimension. Robust expansiveness, quasi-Anosov diffeomorphisms. Fathi's metric for expansive homeomorphisms: topological entropy of expansive homeomorphisms. Variations on the concept of expansiveness: cw-exp, h-exp, measure-exp, N-exp, countable-exp, hyper-exp. 2-expansiveness on surfaces. Robust N-expansiveness on C^r topology. Local conectedness on cwexp of surfaces.
Cronograma: Quatro aulas de duas horas, com exercícios,
Horário: Entre 10:00 e 12:00.
Período: De 15 a 18 de fevereiro de 2016.
Local: Sala C116, bloco C do Centro de Tecnologia, campus da Ilha do Fundão.
Bibliografia:
Notes to be prepared by Artigue and Vieitez.
N. Aoki and K. Hiraide, Topological theory of dynamical systems, North-Holland, 1994.
A. Artigue, J. Brum, and R. Potrie, Local product structure for expansive homeomorphisms, Topology Appl. 156 (2009).
A. Artigue, Hyper-expansive homeomorphisms, Publicaciones Matemáticas del Uruguay 14 (2013).
A. Artigue, M. J. Pacífico, and J. L. Vieitez, N-expansive homeomorphisms on surfaces, Communications in Contemporary Mathematics (2014).
R. Bowen, Entropy-expansive maps, Trans. of the AMS 164 (1972).
A. Fathi, Expansiveness, hyperbolicity and Hausdor dimension, Commun. Math. Phys. 126 (1989).
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math. 27 (1990).
H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math. 45 (1993). -J.
Lewowicz, Lyapunov Functions and Topological Stability, J. Di. Eq. 38 (1980).
J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Bras. Mat. 20 (1989).
R. Man~é, Expansive diffeomorphisms, Dynamical SystemsWarwick 1974, 1975.
R. Man~é, Expansive homeomorphisms and topological dimension, Trans. of the AMS 252 (1979).
C. A. Morales and V. F. Sirvent, Expansive measures, 29o Colóq. Bras. Mat., IMPA, 2013.
C. A. Morales, A generalization of expansivity, Discrete Contin. Dyn. Syst. 32 (2012).
M. J. Pacifico, E. R. Pujals, M. Sambarino, and J. L.Vieitez, Robustly expansive codimensionone homoclinic classes are hyperbolic, Ergodic Theory Dynam. Systems 29 (2009).
M. J. Pacifico, E. R. Pujals, and J. L. Vieitez, Robustly expansive homoclinic classes, Ergodic Theory Dynam. Systems 25 (2005).
M. J. Pacifico and J. L. Vieitez, Entropy expansiveness and domination for surface diffeomorphisms, Rev. Mat. Complut. 21 (2008), no. 2.
W. R. Utz, Unstable homeomorphisms, Proc. Amer. Math. Soc. 1 (1950), no. 6.
J. L. Vieitez, Expansive homeomorphisms and hyperbolic dieomorphisms on 3-manifolds, Ergod Theory Dynam. Systems 16 (1996).
J. L. Vieitez, Lyapunov functions and expansive diffeomorphisms on 3D-manifolds, Ergod Theory Dynam. Systems 22 (2002),

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