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Nonstandard analysis of global attractors
Author(s) -
Pražák Dalibor,
Slavík Jakub
Publication year - 2015
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201400029
Subject(s) - attractor , mathematical proof , social connectedness , key (lock) , mathematics , simple (philosophy) , set (abstract data type) , limit set , limit (mathematics) , calculus (dental) , pure mathematics , computer science , epistemology , mathematical analysis , programming language , medicine , psychology , philosophy , geometry , computer security , dentistry , psychotherapist
Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness. The key observation is that the global attractor, or more generally, the ω‐limit set, can be written as a standard part of a suitable internal set.