Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 16, Issue 5, Pages 1151-1191Publisher
SPRINGER
DOI: 10.1007/s10208-015-9272-x
Keywords
Attractor; Attracting neighborhood; Invariant set; Distributive lattice; Birkhoff's representation theorem
Funding
- NSF [NSF-DMS-0914995, NSF-DMS-0835621, 0915019, 1125174, 1248071]
- AFOSR
- DARPA
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1125174] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1248071, 0915019] Funding Source: National Science Foundation
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The algebraic structure of the attractors in a dynamical system determines much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics, which are capable of computing attracting neighborhoods efficiently. Here we address the question of whether all of the algebraic structure of attractors can be captured by these methods.
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