Dominated Splittings for Flows with singularities
Vitor Araujo, Alexander Arbieto, Luciana Salgado
TL;DR
This paper establishes conditions under which invariant splittings in flows with singularities are dominated, simplifying the criteria needed for sectional hyperbolicity and hyperbolicity in dynamical systems.
Contribution
It provides new sufficient conditions for dominated splittings in flows with singularities, reducing the complexity of verifying hyperbolic structures.
Findings
Sufficient conditions for dominated splittings in flows with singularities.
Reduction of requirements for sectional hyperbolicity.
Enhanced criteria for hyperbolicity in dynamical systems.
Abstract
We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a flow to be dominated. In particular, we reduce the requirements to obtain sectional hyperbolicity and hyperbolicity.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems