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Pedro Duarte

Bio: Pedro Duarte is an academic researcher from University of Lisbon. The author has contributed to research in topics: Lyapunov exponent & Ergodic theory. The author has an hindex of 19, co-authored 100 publications receiving 934 citations. Previous affiliations of Pedro Duarte include Instituto Superior Técnico & Technical University of Lisbon.


Papers
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Journal ArticleDOI
TL;DR: For the Standard Map, a well-known family of conservative diffeomorphisms on the torus, this paper constructed large basic sets which fill in the toros as the parameter runs to ∞ and proved that these basic sets are accumulated by elliptic periodic islands.

125 citations

Book
24 Mar 2016
TL;DR: In this article, the Oseledets Filtration and Decomposition of Grassmann Manifolds is discussed. But the authors focus on large deviations for random Cocycles.
Abstract: Introduction.- Estimates on Grassmann Manifolds.- Abstract Continuity of Lyapunov Exponents.- The Oseledets Filtration and Decomposition.- Large Deviations for Random Cocycles.- Large Deviations for Quasi-Periodic Cocycles.- Further Related Problems.

69 citations

Journal ArticleDOI
TL;DR: In this paper, a conservative analogue of the theorem of Newhouse on the abundance of wild hyperbolic sets is proved, and it is shown that for a residual subset in an open set of nearby systems, these basic sets are accumulated by periodic elliptic islands.
Abstract: We prove a conservative analogue of a theorem of Newhouse on the abundance of wild hyperbolic sets: Arbitrarily close to any area preserving map with a homoclinic tangency there are maps with 'wild' hyperbolic sets having persistent homoclinic tangencies. Furthermore, for a residual subset in an open set of nearby systems, these basic sets are accumulated by periodic elliptic islands.

57 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide an overview on the assessment of fatigue life of marine engine crankshafts and its maintenance taking into account the design improving in the last decades, considering that accurate estimation of the fatigue life is very important to ensure safety of components and its reliability.

53 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that every one-parameter family of area-preserving maps unfolding a homoclinic tangency has a sequence of parameter intervals approaching the bifurcation parameter, where the dynamics exhibits wild hyperbolic sets accumulated by elliptic isles.
Abstract: We prove that every one-parameter family of area-preserving maps unfolding a homoclinic tangency has a sequence of parameter intervals, approaching the bifurcation parameter, where the dynamics exhibits wild hyperbolic sets accumulated by elliptic isles. This is a parametric conservative analogue of a famous theorem of Newhouse on the abundance of wild hyperbolic sets.

46 citations


Cited by
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Book ChapterDOI
01 Jan 1977
TL;DR: In the Hamadryas baboon, males are substantially larger than females, and a troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young.
Abstract: In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

2,364 citations

Book ChapterDOI
15 Feb 2011

1,876 citations

01 Jan 1996

1,282 citations

Book ChapterDOI
01 Jan 2003
TL;DR: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas and there is no doubt that a modern treatise on “Nonlinear functional analysis” can not afford the luxury of ignoring multivalued analysis.
Abstract: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

996 citations