The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 53-746
Full Name: Eleonora Catsigeras
Position: Associate Professor
Age: ON
Sex: Female
Address: Av. Herrera y Reissig 565 C.P.11300 Montevideo
Country: URUGUAY
Tel: 2711-0621
Tel prefix: +598
Fax: 2711-4462
E-mail address: eleonora@fing.edu.uy
Other E-mails: eleonora17@gmail.com
Title of the Paper: Ergodic Theorems Respect to Lebesgue
Authors as they appear in the Paper: Eleonora Catsigeras
Email addresses of all the authors: eleonora@fing.edu.uy
Number of paper pages: 20
Abstract: We study, from the ergodic viewpoint, the asymptotic dynamics in the future of a full Lebesgue set of initial states. The dynamical systems under research are deterministic and evolving with discrete time n, by the forward iterations of any continuous map f acting on a finite-dimensional, compact and Riemannian manifold M. First, we revisit the classic denition of physical or SRB probability measures, and its generalized notion of weak physical probabilities. Then, inspired in the statistical meaning of the ergodic attractors defined by Pugh and Schub, which support ergodic physical measures, we define the more general concept of ergodic-like attractor. We prove that any such generalized attractor is the support of weak physical probabilities and conversely. Then, we revisit the proof of existence of weak physical probabilities and conclude that any continuous dynamics exhibits at least one ergodic-like attractor.
Keywords: Ergodic theory, Physical measures, Ergodic attractors, Topological dynamics, Theoretical measure
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How Did you learn about congress: Ergodic Theory and abstract Dynamical Systems
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