Ergodic Theory


Convergence in L^p, in measure and a.e.; integrability; Fatou Lemma, Monotone Convergence and Dominated Convergence; isomorphism in measure. Periodic orbit, recurrent, non-wandering, dense; conjugacy, stability. Invariant measures by a dynamic. Invariants by isomorphism. Existence of invariant probability measures for continuous dynamics on compact metric spaces. Ergodicity, mixing, uniquely ergodicity; dynamical and spectral interpretations of these metrical properties. Examples: homeomorphism of R; qx(mod1); Gauss map; shifts; powers of z and rotation in S^1; linear maps in R^n; Anosov diffeomorphisms; Smale horseshoe; pedal triangle; coupled systems; Markov chains; search engines. Poincaré, Birkhoff and Kac Theorems; connection with the second law of Thermodynamics. Applications: Borel Theorem on normal numbers; Multiple Recurrence Theorem; van der Waerden Theorem. Ergodic decomposition. Topological and measure-theoretic entropy. Variational principle and equilibrium states.

Research and Events


  • PhD Defense
    Fernando Lucatelli Nunes - Pseudomonads and Descent
    10:00 - Sala dos Capelos, Univ. Coimbra
    January 24, 2018
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Defended Theses

  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
  • Representations of generalized quivers
      Artur Duarte Ferreira de Araújo (June 2017)
      Peter Gothen
  • On semisimple Hopf actions
      Deividi Ricardo Pansera (June 2017)
      Christian Edgar Lomp
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