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Author

Jorge Milhazes Freitas

Other affiliations: University of Porto
Bio: Jorge Milhazes Freitas is an academic researcher from University of Madeira. The author has contributed to research in topics: Dynamical systems theory & Extreme value theory. The author has an hindex of 24, co-authored 77 publications receiving 1789 citations. Previous affiliations of Jorge Milhazes Freitas include University of Porto.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors show that a multimodal map with an invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example).
Abstract: We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes.

169 citations

Book
25 Apr 2016
TL;DR: In this article, the authors provide a broad overview of the interdisciplinary research area of extreme events, underlining its relevance for mathematics, natural sciences, engineering, and social sciences, and discuss how extreme events can be used as probes for inferring fundamental dynamical and geometrical properties of a dynamical system.
Abstract: This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its relevance for mathematics, natural sciences, engineering, and social sciences. After exploring the basics of the classical theory of extreme events, the book presents a careful examination of how a dynamical system can serve as a generator of stochastic processes, and explores in detail the relationship between the hitting and return time statistics of a dynamical system and the possibility of constructing extreme value laws for given observables. Explicit derivation of extreme value laws are then provided for selected dynamical systems. The book then discusses how extreme events can be used as probes for inferring fundamental dynamical and geometrical properties of a dynamical system and for providing a novel point of view in problems of physical and geophysical relevance. A final summary of the main results is then presented along with a discussion of open research questions. Finally, an appendix with software in Matlab programming language allows the readers to develop further understanding of the presented concepts.

165 citations

Posted Content
TL;DR: In this article, the authors show that a multimodal map with an invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example).
Abstract: We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes.

133 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the extremal index is associated with periodic behaviour and the existence of hitting time statistics for balls around periodic points in a dynamical system with respect to various measures.

115 citations


Cited by
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01 Jan 2016
TL;DR: An introduction to the theory of point processes is universally compatible with any devices to read and will help you get the most less latency time to download any of the authors' books like this one.
Abstract: Thank you for downloading an introduction to the theory of point processes. As you may know, people have search hundreds times for their chosen novels like this an introduction to the theory of point processes, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some harmful virus inside their computer. an introduction to the theory of point processes is available in our digital library an online access to it is set as public so you can download it instantly. Our book servers hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of point processes is universally compatible with any devices to read.

903 citations

01 Jan 1997

892 citations

Journal ArticleDOI
TL;DR: Two important results refer to the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum and the need for coupled modeling of natural and socio-economic systems.
Abstract: We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models The applications include climatic, seismic and socio-economic events, along with their prediction Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems Both these results have implications for the study and prediction of natural hazards and their human impacts

193 citations