Every invertible, measure-preserving dynamical system induces a Koopman operator, which
is a linear, unitary evolution operator acting on the L 2 space of observables associated with …

Rotational invariant circles of area-preserving maps are an important and well-studied
example of KAM tori. John Greene conjectured that the locally most robust rotational circles …

In this paper, we develop numerical methods based on the weighted Birkhoff average for
studying two-dimensional invariant tori for volume-preserving maps. The methods do not …

The Birkhoff ergodic theorem concludes that time averages, ie Birkhoff averages, ${\rm B}
_N (\, f):=\Sigma_ {n= 0}^{N-1} f (x_n)/N $ of a function f along a length N ergodic trajectory …

This paper investigates the utility of the weighted Birkhoff average (WBA) for distinguishing
between regular and chaotic orbits of flows, extending previous results that applied the WBA …

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We
propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the …

The analysis of a timeseries can provide many new perspectives if it is accompanied by the
assumption that the timeseries is generated from an underlying dynamical system. For …

In this paper, we distinguish between four categories of dynamics for quasiperiodically-
forced (QPF) circle maps: resonant and incommensurate regular dynamics, and strongly and …

A dynamical system is a transformation of a phase space, and the transformation law is the
primary means of defining as well as identifying the dynamical system. It is the object of …

The E× B drift motion of particles in tokamaks provides valuable information on the
turbulence-driven anomalous transport. One of the characteristic features of the drift motion …