Proportions of incommensurate, resonant, and chaotic orbits for torus maps.

This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular, between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold's circle map, for which there is a universal power law for the fraction of nonresonant orbits as a function of the amplitude of the nonlinearity. Our methods give a more precise calculation of the coefficients for this power law.

[Medical electroradiology technicians: mediators in hospital care].

Beyond simply carrying out the medical imaging procedure, radiology technicians have an ambivalent position in radiology departments: working both with the patient and with the doctor, they act as a link between these two entities which rarely, if ever, meet. This socioprofessional category is a keystone to medical imaging services, yet it receives little recognition and its crucial role is often overlooked. The exact delimitation of its functions within the hospital is often misunderstood.

The three-dimensional generalized Hénon map: Bifurcations and attractors.

We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark-Sacker bifurcations, give rise to Arnold tongues in parameter space.

Toward automated extraction and characterization of scaling regions in dynamical systems.

Scaling regions-intervals on a graph where the dependent variable depends linearly on the independent variable-abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent. In these applications, scaling regions are generally selected by hand, a process that is subjective and often challenging due to noise, algorithmic effects, and confirmation bias. In this paper, we propose an automated technique for extracting and characterizing such regions.

Nonexistence of invariant tori transverse to foliations: An application of converse KAM theory.

Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay's converse Kolmogorov-Arnol'd-Moser condition to obtain a sufficient condition for the nonexistence of invariant surfaces that are transverse to a chosen 1D foliation. We show how useful foliations can be constructed from approximate integrals of the system.