Measure synchronization in dynamical system: A critical assessment

Abstract

This paper aims to review the measure synchronization observed in coupled Hamiltonian systems briefly. The word `measure' implies the Lebesgue measure, which generalizes the notion of length, area, and volume in Euclidean space. During the measure synchronized state, each system shares a phase space domain with an identical invariant measure. Measure synchronization is characterized by a Hamiltonian system that displays either quasiperiodic or chaotic dynamics. This synchronization has been observed in various physical systems, such as coupled pendula, Josephson junctions, and lasers.Comment: 9 pages, 3 figure