Robust Transitivity in Hamiltonian Dynamics

A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting "large" robustly transitive sets. We show that the $C^\infty$ closure of such open sets contains a variety of systems, including so-called a priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is a combination of studying minimal dynamics of symplectic iterated function systems and a new tool in Hamiltonian dynamics which we call symplectic blender.Comment: 52 pages, 3 figure

Prime ends rotation numbers and periodic points

We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\'eordory's prime ends rotation number, similar to Poincar\'e's theory for circle homeomorphisms. In particular, we prove the converse of a classic result of Cartwright and Littlewood. This has a number of consequences for generic area preserving surface diffeomorphisms. For instance, we extend previous results of J. Mather on the boundary of invariant open sets for $C^r$-generic area preserving diffeomorphisms. Most results are proved in a general context, for homeomorphisms of arbitrary surfaces with a weak nonwandering-type hypothesis. This allows us to prove a conjecture of R. Walker about co-basin boundaries, and it also has applications in holomorphic dynamics.Comment: 50 pages, 15 figure

Estrategias para el desarrollo de la diplomacia deportiva internacional en la federación de voleibol de la República Islámica de Irán

In recent years, Iran's volleyball sport has made significant progress and the Iranian national team has been able to compete in the World Volleyball League.This situation has provided the Iranian Volleyball Federation with diplomatic opportunities.The purpose of this study was to develop strategies for the development of international sport diplomacy in the volleyball federation of the Islamic Republic of Iran.This study was conducted qualitatively by interviewing Iranian volleyball officials (N = 4), academic experts in sport diplomacy (N = 4) and internationally experienced coaches and referees (N = 5).Data analysiswith theme analysis techniques revealed that the five emerging themes included: challenges, principles of effective international sport diplomacy, international sport diplomacy success factors, international diplomacy development strategies in volleyball federation, and the implications of international sport diplomacy, including 18 sub-themes and 43 open codes.All these aspects are analyzed and discussed in the present study.En los últimos años, el deporte de voleibol ha logrado un progreso significativo en Irán y el equipo nacional iraní ha podido competir en la Liga Mundial de Voleibol. Esta situación ha brindado oportunidades diplomáticas a la Federación Iraní de Voleibol. El propósito de este estudio fue desarrollar estrategias para el desarrollo de la diplomacia deportiva internacional en la federación de voleibol de la República Islámica de Irán. Este estudio se realizó de forma cualitativa entrevistando a funcionarios de voleibol iraníes (N = 4), expertos académicos en diplomacia deportiva (N = 4) y entrenadores y árbitros con experiencia internacional (N = 5). El análisis de datos con técnicas de análisis temático reveló que los cinco temas emergentes incluían: desafíos, principios de la diplomacia deportiva internacional efectiva, factores de éxito de la diplomacia deportiva internacional, estrategias de desarrollo de la diplomacia internacional en la federación de voleibol y las implicaciones de la diplomacia deportiva internacional, incluyendo 18 subtemas y 43 códigos abiertos. Todos estos aspectos se analizan y discuten en el presente estudio