We apply I Mather's theory on minimizing measures to the case of positive definite autonomous Lagrangians L : TM -f R. We show that the minimal action function @(h) = min(J'Ldp(pQ = h), has radial derivative, p(p) E H](M,R) is the homology vector of the invariant probability p. As one consequence, for any supporting domain S of p , the closure of the union of the support of any minimizing measures with homology in S is contained in a fixed energy level. It is also shown that there is a one-to-one correspondence between minimizing measures for Lagrangians associated to mechanical systems (kinetic minus potentid energy) and mirimizing m w e s for the geodesic problem on a fired energy level.

This paper addresses the question of genericity of existence of elliptic islands for the billiard map associated to strictly convex closed curves. More precisely, we study 2-periodic orbits of billiards associated to C 5 closed and strictly convex curves and show that the existence of elliptic islands is a dense property on the subset of those billiards having an elliptic 2-periodic point. Our main tools are normal perturbations, the Birkhoff Normal Form for elliptic fixed points and Moser's Twist Theorem.

In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period N , all nondegenerate. Moreover, the stable and unstable manifolds of hyperbolic points are transversal. We explore these properties to give some dynamical consequences especially about the dynamics in the instability regions.

Recent studies have documented the high prevalence of burnout among medicine and dentistry students, with potentially catastrophic consequences for both students and patients. Both environmental and personality factors play a part in burnout; perfectionism, a common trait in medicine students’ personalities, has been linked to psychological distress and increasing students’ vulnerability to burnout. Self-compassion, i.e., treating oneself kindly through hardship, has recently emerged as a buffer between perfectionism and psychological distress. While using a novel three-factor conceptualization of perfectionism (BIG3), this study aims to analyze if self-compassion has a protective role in the relationship between perfectionism and burnout, in a sample of medicine and dentistry students, through mediation analysis. We found that self-compassion significantly mediated the relationship between all three forms of perfectionism and burnout: as a partial mediator in self-critical and rigid perfectionism, as well as a full mediator in narcissistic perfectionism. Our findings underline self-compassion’s relevance in burnout prevention and management, supporting its use as an intervention target in burnout reduction programs and strategies.

In this paper we show the existence of a plateau for the minimal action function associated with a model for a particle under the influence of a magnetic field (Hall effect). We will describe the structure of the Mather sets, that is, sets that are support of minimizing measures for the corresponding autonomous Lagrangian. This description is obtained by constructing a twist map induced by the first return map associated with a certain transversal section on a fixed level of energy.