TL;DR
This paper introduces abstract hyperbolic sets and a new symbolic dynamics approach to better understand chaos, aiming to clarify complex chaotic behaviors and inspire new models.
Contribution
It presents a novel perspective on hyperbolic chaos using symbolic dynamics without focusing on mappings or convergence rates.
Findings
Introduction of abstract hyperbolic sets
New symbolic dynamics paradigm for chaos
Potential for revisiting and creating models
Abstract
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our suggestions are for more neat comprehension of chaos in the domain. The novelties can serve for revisited models as well as motivate new ones.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization