Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

alr approach for replacing values below the detection limit

All of the imputation techniques usually applied for replacing values below thedetection limit in compositional data sets have adverse effects on the variability. In thiswork we propose a modification of the EM algorithm that is applied using the additivelog-ratio transformation. This new strategy is applied to a compositional data set and theresults are compared with the usual imputation techniques

On the number of limit cycles bifurcating from a non-global degenerated center

Vegeu el resum a l'inici del document del fitxer adjunt

Lower bounds for the number of limit cycles of trigonometric Abel equations

"Vegeu el resum a l'inici del document del fitxer adjunt"

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

"Vegeu el resum a l'inici del document del fitxer adjunt."

Limit Cycles for a class of three dimensional polynomial differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the upper bound of the number of limit cycles obtained by the second order averaging method I

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the upper bound of the number of limit cycles obtained by the second order averaging method II

"Vegeu el resum a l'inici del document del fitxer adjunt."

Geometric tools to determine the hyperbolicity of limit cycles

"Vegeu el resum a l'inici del document del fitxer adjunt."

Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

"Vegeu el resum a l´inici del document del fitxer adjunt."

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Maximal operators and differentiation theorems for sparse sets

"Vegeu el resum a l'inici del document del fitxer adjunt."