Abstract
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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Communicated by Richard Schwartz.
The first author is partially supported by NSF Grant NSF-DMS-0914995, the second author is partially supported by NSF Grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. The present work is part of the third authors activities within CAST, a Research Network Program of the European Science Foundation ESF.
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Kalies, W.D., Mischaikow, K. & Vandervorst, R.C.A. Lattice Structures for Attractors II. Found Comput Math 16, 1151–1191 (2016). https://doi.org/10.1007/s10208-015-9272-x
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DOI: https://doi.org/10.1007/s10208-015-9272-x