We prove an embedding theorem for maps from a finite complex into a Poincaré duality space. The proof uses fiberwise homotopy theory.

In this study, the influence of leg rotation during the swing phase on the stability of running is addressed. Therefore, conservative spring-mass running was investigated using a return map of the apex height. A fixed angle of attack can already result in selfstabilised running as found previously. By examining the return maps of all possible angles of attack, a rotational leg control is derive...

In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.

We study a family of area-preserving maps of the 2-torus and show that they are pseudo-Anosov. We present a method to construct finite Markov partitions for this family which utilizes their common symmetries. Through these partitions we show explicitly that each map is a tower over a first return map, intimately linked to a toral automorphism. This enables us to calculate directly some dimensio...

The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...

We work with a perturbed fractional differential equation discontinuous right-hand sides where discontinuity function crosses boundary transversally. The corresponding Poincaré map in neighbourhood of periodic orbit an unperturbed is found. Then, bifurcations solutions are analysed together concrete example.

1. The object of this note is to announce a theory of surgery on Poincaré and normal spaces, with applications to Poincaré geometry and manifolds. The present point of view on Poincaré surgery was outlined by W. Browder in the spring of 1969, and is purely homotopy-theoretic. The main missing ingredient in the program was Lemma 1.5, and the (considerable) machinery required for its application....

This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive...

This paper is devoted to a mathematical analysis of a route to chaos for bounded piecewise smooth systems of dimension three subjected to symmetric non-smooth bifurcations. This study is based on period doubling method applied to the associated Poincaré maps. Those Poincaré maps are characterized taking into account the symmetry of the transient manifolds. The corresponding Poincaré sections ar...

We calculated Eq. (4) by using the Runge-Kutta method. The attractors obtained by the simulations are shown in Fig. 3(a). We can confirm the generation of periodic and chaotic attractors. In order to investigate the attractors in van der Pol oscillator under noisy parametric excitation in detail, we consider the Poincaré map. The result of the Poincaré map are shown in Fig. 3(b). We can see tha...