Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Performance of Layers Submitted to Different Forced Molting Methods and Different Temperatures

This study was carried out to evaluate the performance and egg quality of laying hens, in their second laying cycle submitted to different forced-molting methods and three environmental temperatures. Six hundred layers were distributed in a completely randomized experimental design with 15 treatments with five replicates of eight birds each, according to 5x3 factorial arrangement (molting methods vs. temperatures). The following forced-molting methods were applied: 90%, 70%, 50% dietary alfalfa inclusion, addition of 2,800 ppm zinc, and feed fasting. Temperatures were: 20 degrees C, 27 degrees C and 35 degrees C. At the end of each period of the second laying cycle, bird performance and egg quality were evaluated. Data were submitted to analysis of variance and means were compared by orthogonal and polynomial contrasts. The highest alfalfa inclusion level (90% alfalfa and 10% basal diet) proved to be efficient as compared to the other methods, independently of temperature.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)