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 …

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 …

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

In this paper, we focus on distinguishing between the types of dynamical behavior that occur
for typical one-and two-dimensional torus maps, in particular without the assumption of …

This work provides a systematic recipe for computing accurate high order Fourier
expansions of quasiperiodic invariant circles (and systems of such circles) in area …

This paper presents a methodology to study non-twist invariant circles and their bifurcations
for area preserving maps, which is supported on the theoretical framework developed in …

A dynamical system may be defined by a simple transition law-such as a map or a vector
field. The objective of most learning techniques is to reconstruct this dynamic transition law …

A discrete-time deterministic dynamical system is governed at every step by a
predetermined law. However the dynamics can lead to many complexities in the phase …

Significant progress has been made in designing magnetic fields that provide excellent
confinement of the guiding-centre trajectories of alpha particles using quasisymmetry (QS) …