Víctor Jiménez López

Global attractors for difference equations dominated by one-dimensional maps

The global attractivity character of nonlinear higher order difference equations of the form is investigated when g is dominated by an interval scalar map. Some basic properties of the interval map are obtained and used to prove new global attractivity criteria for the above equation with no monotonicity restrictions on g. Our results are applied to many models from mathematical biology and economy. The derived global attractivity criteria of these models are either new or improve substantially known ones.

Transitive flows on manifolds

In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name

The influence of the percentage of the common limb in weight loss and nutritional alterations after laparoscopic gastric bypass

BACKGROUND Roux-en-Y gastric bypass (RYGB) is considered the gold standard for the treatment of morbid obesity. There is no consensus over ideal limb length when the bypass is created and published studies do not take into account the influence of the common limb (CL) on weight loss. The objective was to study the influence of the common limb after RYGB. The setting was the Virgen de la Arrixaca University Clinical Hospital in Murcia, Spain. MATERIAL AND METHODS This prospective study includes 151 patients undergoing laparoscopic RYGB surgery for morbid obesity. The patients were divided into 2 groups according to their body mass index. The small intestine (SI) was measured using micro forceps so that the percentage of common limb (%CL) could then be compared against the total SI in each patient. The percentage of excess weight loss (%EWL) in relation to the %CL was calculated at 3, 12, and 24 months. A series of tests was conducted simultaneously to analyze nutritional deficiencies and their relation to the %CL. RESULTS The total jejunoileal segment and the %CL in the groups of both obese and super-obese patients had no influence on the %EWL in either group for any of the periods studied. The patients with a %CL<50% had greater nutritional deficiencies in the follow-up period and required supplements and more frequent laboratory tests. CONCLUSIONS The %CL has no effect on weight loss in RYGB patients. A lower %CL is related to greater nutritional deficiencies.

There are no piecewise linear maps of type 2

The aim of this paper is to show that there are no piecewise linear maps of type 2∞. For this purpose we use the fact that any piecewise monotone map of type 2∞ has an infinite ω-limit set which is a subset of a doubling period solenoid. Then we prove that piecewise linear maps cannot have any doubling period solenoids.

LARGE CHAOS IN SMOOTH FUNCTIONS OF ZERO TOPOLOGICAL ENTROPY

In 1975, the notion of chaos in the sense of Li and Yorke was introduced [9]. Anequivalent and simpler formulation of this concept has been given in [8].DEFINITION: Let I denote a compact real interval an —d> / le bt /e a: I contin-uous function. Suppose that there exist 8^0 and S C I with at least two elementssuch that for any x, y £ S, x ^ y, and any periodic point p of /:

Accumulation points of nonrecurrent orbits of surface flows

Abstract In this paper we characterize topologically ω -limit sets of nonrecurrent orbits of flows on compact connected surfaces. As a particular case, ω -limit sets are fully characterized for the Klein bottle, the projective plane and the sphere.

All maps of type 2^{∞} are boundary maps

Let f be a continuous map of an interval into itself having periodic points of period 2n for all n ≥ 0 and no other periods. It is shown that every neighborhood of f contains a map g such that the set of periods of the periodic points of g is finite. This answers a question posed by L. S. Block and W. A.

Is Trivial Dynamics That Trivial

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PARADOXICAL FUNCTIONS ON THE INTERVAL

In this paper it is shown that any expanding with Lipschitz deriva- tive function / has a contradictory behaviour from the point of view of chaos in the sense of Li and Yorke. On the one hand it cannot generate scrambled sets of positive Lebesgue measure. On the other hand the two-dimensional set Ch(/) including the pairs (x, y) such that {x, y} is a scrambled set of / has positive measure. In fact, both the geometric structure (almost everywhere) and measure of Ch(/) can be explicitly obtained.

The Y2K problem revisited

We investigate the stability properties of the second order difference equation This equation has a unique fixed point and it has been conjectured for a long time that all orbits converge to this fixed point. The conjecture has been proved for some values of the parameters p and q. We enlarge this set of parameters by proving the conjecture in the case To do this we use an improved version of a tool (the so-called dominance condition) introduced recently by H. A. El-Morshedy and the author in El-Morshedy and Jiménez López [J. Differ. Equ. Appl. 14 (2008), pp. 291–410]. The general conjecture still remains open.We investigate the stability properties of the second order difference equation This equation has a unique fixed point and it has been conjectured for a long time that all orbits converge to this fixed point. The conjecture has been proved for some values of the parameters p and q. We enlarge this set of parameters by proving the conjecture in the case To do this we use an improved version of a tool (the so-called dominance condition) introduced recently by H. A. El-Morshedy and the author in El-Morshedy and Jimenez Lopez [J. Differ. Equ. Appl. 14 (2008), pp. 291–410]. The general conjecture still remains open.