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math.DS2014
Existence of invariant tori in three dimensional maps with degeneracy
Umesh Vaidya, Igor Mezic
We prove a KAM-type result for the persistence of two-dimensional invariant tori in perturbations of integrable action-angle-angle maps with degeneracy, satisfying the intersection…
math.DS2014
Extreme phase sensitivity in systems with fractal isochrons
Alexandre Mauroy, Igor Mezic
Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this co…
math.DS2014
Global stability analysis using the eigenfunctions of the Koopman operator
Alexandre Mauroy, Igor Mezic
We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can…