The Lyapunov stability of first order dynamic equations with respect to time-dependent Riemannian metrics
G.Sardanashvily
TL;DR
This paper demonstrates that the Lyapunov stability of solutions to first order dynamic equations can be controlled through the selection of suitable time-dependent Riemannian metrics.
Contribution
It introduces a method to achieve Lyapunov stability for first order dynamic equations by choosing appropriate time-dependent Riemannian metrics.
Findings
Lyapunov stability can be induced by metric choice
Time-dependent Riemannian metrics influence stability
Stability is controllable at will
Abstract
Solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Quantum chaos and dynamical systems · Mathematical Biology Tumor Growth