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Computing All Isolated Invariant Sets at a Finite Resolution
Salgado-Flores, Martin
Salgado-Flores, Martin
Abstract
Conley Index theory has inspired the development of rigorous computational methods to study dynamics. These methods construct outer approximations, combinatorial representations of the system, which allow us to represent the system as a combination of two graphs over a common vertex set. Invariant sets are sets of vertices and edges on the resulting digraph. Conley Index theory relies on isolated invariant sets, which are maximal invariant sets that meet an isolation condition, to describe the dynamics of the system. In this work, we present a computationally efficient and rigorous algorithm for computing all isolated invariant sets given an outer approximation. We improve upon an existing algorithm that “grows” iso- lated invariant sets individually and requires an input size of 2n, where n is the number of grid elements used for the outer approximation.
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2016-05-01
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Mathematics