NDLI: Finite Resolution Dynamics

Content Provider	Springer Nature Link
Author	Luzzatto, Stefa Pilarczyk, Paweł
Copyright Year	2011
Abstract	We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given number. Open covers are used to approximate the topology of the phase space in a finite way, and the dynamical system is represented by means of a combinatorial multivalued map. We formulate notions of transitivity and mixing in the finite resolution setting in a computable and consistent way. Moreover, we formulate equivalent conditions for these properties in terms of graphs, and provide effective algorithms for their verification. As an application we show that the Hénon attractor is mixing at all resolutions coarser than 10−5.
Ending Page	239
Page Count	29
Starting Page	211
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	2
Volume Number	11
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-01-20
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Open cover Mixing Economics general Linear and Multilinear Algebras, Matrix Theory Dynamical system Combinatorial dynamics Transitivity Algorithm Finite resolution Numerical chaos Rigorous numerics Numerical Analysis Computer Science Math Applications in Computer Science Applications of Mathematics Directed graph Algorithms with automatic result verification
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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