What is it about?
Nonlinear phenomena in a deterministic framework can be studied in terms of a "pattern" that does not change. This pattern is of topological nature, the hidden "shape" behind time-evolving datasets. This pattern can be described using a dual mathematical object combining a cell complex and a digraph. This new object is called "templex".
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Why is it important?
It enables describing attractor beyond knot theory, which can only be applied for systems with three degrees of freedom, and it also incorporates details in the description which homologies alone cannot capture.
Perspectives
The templex brings to bear advanced physico-mathematical methods on the understanding, description, and prediction of the high-risk effects of global anthropogenic changes.
Denisse Sciamarella
Centre National de la Recherche Scientifique
Read the Original
This page is a summary of: Templex: A bridge between homologies and templates for chaotic attractors, Chaos An Interdisciplinary Journal of Nonlinear Science, August 2022, American Institute of Physics,
DOI: 10.1063/5.0092933.
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