| Campo DC | Valor | Idioma |
|---|
| dc.creator | Santos, Pedro Emanuel Oliveira dos | - |
| dc.date.accessioned | 2024-11-05T11:17:08Z | - |
| dc.date.available | 2025-01-01 | - |
| dc.date.available | 2024-11-05T11:17:08Z | - |
| dc.date.issued | 2024-05-10 | - |
| dc.identifier.citation | SANTOS, Pedro Emanuel Oliveira dos. Formalismo ergódico. 2024. 58 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística - IME, Universidade Federal da Bahia, Salvador (Bahia), 2024. | pt_BR |
| dc.identifier.uri | https://repositorio.ufba.br/handle/ri/40559 | - |
| dc.description.abstract | In this paper we present the concepts of Baire Ergodicity and Ergodic Formalism introduced in \cite{Pi1}.
We use them to study topological attractors and statistical attractors and, in particular, to determine their existence and finiteness.
These concepts are also used to investigate topological attractors of interval maps, even with discontinuities.
To do this, we analyze the attractors of wandering intervals. As a result, we demonstrate the finiteness of non-periodic attractors of $C^2$ applications with discontinuities.
For applications of the interval $C^2$ without discontinuities, we show that the topological and statistical attractors coincide and we calculate the Birkhoff upper mean of continuous functions for generic points. | pt_BR |
| dc.description.sponsorship | Fundação de Amparo a Pesquisa do Estado da Bahia - FAPESB | pt_BR |
| dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES | pt_BR |
| dc.language | por | pt_BR |
| dc.publisher | Universidade Federal da Bahia | pt_BR |
| dc.rights | Acesso Aberto | pt_BR |
| dc.subject | Ergodicidade de Baire | pt_BR |
| dc.subject | Intervalos errantes | pt_BR |
| dc.subject | Formalismo ergódico | pt_BR |
| dc.subject | Atratores topológicos | pt_BR |
| dc.subject | Atratores estatísticos | pt_BR |
| dc.subject | Aplicações do intervalo | pt_BR |
| dc.subject.other | Baire ergodicity | pt_BR |
| dc.subject.other | Wandering intervals | pt_BR |
| dc.subject.other | Ergodic formalism | pt_BR |
| dc.subject.other | Topological attractors | pt_BR |
| dc.subject.other | Statistical at- tractors | pt_BR |
| dc.subject.other | Interval maps | pt_BR |
| dc.title | Formalismo ergódico. | pt_BR |
| dc.title.alternative | Ergodic formalism. | pt_BR |
| dc.type | Dissertação | pt_BR |
| dc.publisher.program | Pós-Graduação em Matemática (PGMAT) | pt_BR |
| dc.publisher.initials | UFBA | pt_BR |
| dc.publisher.country | Brasil | pt_BR |
| dc.subject.cnpq | CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA | pt_BR |
| dc.contributor.advisor1 | Pinheiro, Vilton Jeovan Viana | - |
| dc.contributor.advisor1Lattes | http://lattes.cnpq.br/5377575475537411 | pt_BR |
| dc.contributor.referee1 | Pinheiro, Vilton Jeovan Viana | - |
| dc.contributor.referee1Lattes | http://lattes.cnpq.br/5377575475537411 | pt_BR |
| dc.contributor.referee2 | Brandão, Daniel Smania | - |
| dc.contributor.referee2ID | https://orcid.org/0000-0002-3025-1295 | pt_BR |
| dc.contributor.referee2Lattes | http://lattes.cnpq.br/5416521015640279 | pt_BR |
| dc.contributor.referee3 | Varandas, Paulo Cesar Rodrigues Pinto | - |
| dc.contributor.referee3ID | https://orcid.org/0000-0002-0902-8718 | pt_BR |
| dc.contributor.referee3Lattes | http://lattes.cnpq.br/1450367699820349 | pt_BR |
| dc.creator.Lattes | https://lattes.cnpq.br/7523563070878016 | pt_BR |
| dc.description.resumo | Neste trabalho apresentamos os conceitos de Ergodicidade de Baire e de Formalismo Ergódico introduzidos em \cite{Pi1}.
Utilizamo-los para estudar atratores topológicos e atratores estatísticos e, em particular, para determinar condições de existência e finitude deles.
Estes conceitos também são usados para investigar atratores topológicos de aplica-ções do intervalo, mesmo com descontinuidades.
Para isto, analisamos os atratores de intervalos errantes. Como consequência, demonstramos a finitude de atratores não periódicos de aplicações $C^2$ com descontinuidades.
Para aplicações do intervalo $C^2$ sem descontinuidades, demonstramos que os atratores topológicos e estatísticos coincidem e calculamos a média superior de Birkhoff de funções contínuas para pontos genéricos. | pt_BR |
| dc.publisher.department | Instituto de Matemática | pt_BR |
| dc.relation.references | Arnold, V. I.; Afrajmovich, V. S.; Ilyashenko, Y.; Shilnikov, L. P. Bifurcation Theory and Catastrophe Theory. Berlin, Heidelberg: Springer-Verlag, 1999.
Alseda, L.; Llibre, J.; Misiurewicz, M. Combinatorial Dynamics and Entropy in Dimension One. World Scientific Publishing, 1993 (Advanced Series in Nonlinear Dynamics; 5).
Block, L. S.; Copel, W. A. {Dynamics in One Dimension. Berlin, Heidelberg: Springer-Verlag, 1992.
Blokh, A.M. and Lyubich, M. Non-existence of wandering intervals and structure of topological attractors of one-dimensional dynamical systems II, The smooth case. Erg. Th. and Dynam. Sys. 9,
751-758, 1989
Brandão, P; Palis, J; Pinheiro, V. On the finiteness of attractors for piecewise $C^2$ maps of the interval. Erg. Theo. and Dyn. Sys.. Volume 39, Issue 7, pp. 1784-1804, 2019.
Brandão, P.; Palis, P.; Pinheiro, V. On the finiteness of attractors for one-dimensional maps with discontinuities. Advances in Mathematics, 389, https://doi.org/10.1016/j.aim.2021.107891 (2021).
Brandão, P. Topological attractors of contracting Lorenz maps, Annales de l’Institut Henri Poincaré C, Analyse non lin´eaire, Vol. 35, Issue 5, 1409-1433, 2018.
Coven, E. M.; Mulvey, I. Transitivity and the centre for maps of the circle. Ergod. Th. & Dynam. Sys., 6, 1-8, 1986.
Devaney, R. L. An Introduction to Chaotic Dynamical Systems. Westview Press, 2003.
de Vries, J. Topological Dynamical Systems. Berlin: Walter de Gruyter, 2014 (de Gruyter Studies in Mathematics; 59).
Guckenheimer, J. Sensitive Dependence to Initial Conditions for One Dimensional Maps. Commun. Math. Phys., 70, 133-160, 1979.
Halmos, P. R. Naive Set Theory. New York: Van Nostrand Reinhold Company, 1960. (The University Series in Undergraduate Mathematics).
Kechris, A. S. Classical descriptive set theory. New York: Springer-Verlag, 1995 (Graduate texts in mathematics; 156).
Keller, G.; St. Pierre, M. Topological and measurable dynamics of Lorenz maps, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 333-361, 2001.
Lima, E. L. Espaços Métricos. Rio de Janeiro: Editora do IMPA, 2020 (Projeto Euclides).
Lyubich, M. Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems 1. The case of negative Schwarzian derivative. Ergodic Theory Dynamical Systems, 9, 737-750, 1989.
Mañé, R. Ergodic theory and differentiable dynamics. Berlin, Heidelberg: Springer-Verlag, 1987.
Munkres, J. R. Topology Second Edition. Upper Saddle River, NJ 07458: Prentice Hall, 2000.
de Melo, W.; Strien, S. van. One-Dimensional Dynamics, Springer-Verlag, 1993
Oliveira, K.; Viana, M. Fundamentos da Teoria Ergódica. Rio de Janeiro: SBM, 2014 (Coleção Fronteiras da Matemática).
Palis, J. {A Global View of Dynamics and a Conjecture on the Denseness of Finitude of Attractors,
Astérisque, France, v. 261, p. 339-351, 2000.
Palis, J. A global perspective for non-conservative dynamics. Annales de l’Institut Henri Poincaré. Analyse Non Linéaire, 22, p. 487-507, 2005
Pinheiro, V. Ergodic Formalism for topological Attractors and historic behavior. Preprint, 2021.
Pinheiro, V. Topological and statistical attractors for interval maps. Preprint, arXiv:2109.04579, 2021.
Ruelle, D. Historical behaviour in smooth dynamical systems. In B. Krauskopf, H. Broer, and G. Vegter, editors, Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday, pages 63-65. Taylor \& Franci, 2001.
Ruette, S. CHAOS ON THE INTERVAL a survey of relationship between the various kinds of chaos for continuous interval maps. Preprint, 2018.
St. Pierre, M. Topological and measurable dynamics of Lorenz maps. Dissertationes Mathematicae, 382, 1-134, 1999
Takens, F. Orbits with historic behaviour, or non-existence of averages. Nonlinearity, 21(3): T33, 2008.
Strien, S. van; Vargas, E. Real bounds, ergodicity and negative Schwarzian for multimodal maps. J. Am. Math. Soc. 17, 749-782. 2004
Walters, P. An introduction to ergodic theory. New York: Springer-Verlag, 1982. (Graduate texts in mathematics; 79). | pt_BR |
| dc.type.degree | Mestrado Acadêmico | pt_BR |
| Aparece nas coleções: | Dissertação (PGMAT)
|
