We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic fl...

BACKGROUND Physiologic signals, such as cardiac interbeat intervals, exhibit complex fluctuations. However, capturing important dynamical properties, including nonstationarities may not be feasible from conventional time series graphical representations. METHODS We introduce a simple-to-implement visualisation method, termed dynamical density delay mapping ("D3-Map" technique) that provides a...

A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and analyze the Poincare map of the randomly perturbed periodic motion. We show that the time of the first exit from a small neighborhood of the fixed point of the ma...

In this paper, stability analysis of walking gaits and robustness analysis are developed for a five-link and four-actuator biped robot. Stability conditions are derived by studying unactuated dynamics and using the Poincaré map associated with periodic walking gaits. A stable gait is designed by an optimization process satisfying physical constraints and stability conditions. Also, considering...

The paper analyses the nature of limit cycles induced through the interaction of transformer tap changing and load dynamics. Linearization of a Poincaré map is used to prove local stability. An approximation is introduced which allows the map to be formulated explicitly. An estimate of the region of attraction can then be obtained.

We apply the concept of the Euler-Poincaré characteristic and the periodicity number to the index map of an isolated invariant set in order to obtain a new criterion for the existence of periodic points of a continuous map in a given set.

We consider the problem to reconstruct a wave speed c ∈ C∞(M) in a domain M ⊂ R from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map Λ. We introduce a reconstruction formula for c that is based on the Boundary Control method and incorporates features also from the complex geometric optics solutions approach. Moreover, we show that the reconstruction formula is...

Provably asymptotically stable running gaits are developed for the five-link, four-actuator bipedal robot, RABBIT. A controller is designed so that the Poincaré return map associated with periodic running gaits can be computed on the basis of a model with impulse effects that, previously, had been used only for the design of walking gaits. This feedback design leads to the notion of a hybrid ze...

The aim of this work is to study discontinuous one-dimensional maps in the case of slopes and offsets having opposite signs. Such models represent the dynamics of applied systems in several disciplines. We analyze in particular attracting cycles, their border collision bifurcations and the properties of the periodicity regions in the parameter space. The peculiarity of this family is that we ca...

This paper studies rich superstable phenomena in a nonautonomous piecewise constant circuit including one impulsive switch. Since the vector field of circuit equation is piecewise constant, embedded return map is piecewise linear and can be described explicitly in principle. As parameters vary the map can have infinite extrema with one flat segment. Such maps can cause complicated periodic orbi...