Universality of Dynamical Symmetries in Chaotic Maps

Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2024-11, Vol.26 (11), p.969
Main Authors: Acero, Marcos, Lyons, Sean, Aragoneses, Andrés, Pattanayak, Arjendu K
Format: Article
Language:English
Subjects:
Analysis
Asymmetry
Chaos theory
chaos, iterative maps
Complexity
dynamical symmetries
Dynamical systems
Entropy
Mappings (Mathematics)
ordinal patterns
permutation entropy
Symmetry
Symmetry groups
Time series
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Summary:Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a "symmetry space", providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions.
ISSN:1099-4300
1099-4300
DOI:10.3390/e26110969