FERNÁNDEZ SÁNCHEZ , Fernando

Las válvulas de vacío son actualmente un dispositivo cuyo uso ha quedado prácticamente limitado al audio. Desde los comienzos de la electrónica, las válvulas han dado la solución a los problemas de amplificación, siendo de gran ayuda para los diseñadores de amplificadores e instrumentos y obviamente para los músicos. El estudio de estos...

Premio Extraordinario de Doctorado US

The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and often no alternative ways to solve it are searched for. For instance, since linear systems of differential...

The already proved Lum–Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel characterization for Poincaré half-maps in planar linear systems. This proof is very short and...

This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré half-maps, their series expansions (Taylor and Newton–Puiseux) at the tangency point and at infinity, the relative position between the graph of Poincaré half maps and...

We close the problem of the existence of crossing period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic operations on the parameters.

In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line except for at most one point. In the research literature, many papers deal with the problem of determining...

The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been subject of interest of hundreds of papers. After more than 30 years of investigation since Lum–Chua's work, it has remained an open question whether this uniform upper...

The proof of the existence of a global connection in differential systems is generally a difficult task. Some authors use numerical techniques to show this existence, even in the case of continuous piecewise linear systems. In this paper we give an analytical proof of the existence of a reversible T-point heteroclinic cycle in a continuous...

Presentamos en esta comunicación una técnica para probar de forma analítica la existencia de conexiones globales en sistemas dinámicos continuos lineales a trozos. Más concretamente, utilizamos esta técnica para demostrar la existencia de dos conexiones homoclinas directas (aquellas que cortan al plano de separación exactamente dos veces) y un...

En el trabajo comentado, los autores presentan diez sistemas autónomos no lineales caóticos, de los que afirman que no tienen caos en el sentido de Shilnikov. Desgraciadamente, esta afirmación carece de fundamento pues utilizan un teorema erróneo de la literatura.

Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system,...

In this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of homoclinic connections arise from the point of...