Lipschitz inverse shadowing for nonsingular flows
Dmitry Todorov
TL;DR
This paper establishes that for nonsingular flows, the property of Lipschitz inverse shadowing is equivalent to the system being structurally stable, linking a shadowing property to a fundamental stability concept.
Contribution
The paper proves the equivalence between Lipschitz inverse shadowing and structural stability for nonsingular flows, providing a new characterization of stability in dynamical systems.
Findings
Lipschitz inverse shadowing implies structural stability.
Structural stability implies Lipschitz inverse shadowing.
Equivalence between these properties for nonsingular flows.
Abstract
We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization