Physical Conditioning for Combat Sports: book review

Abstract:The present work analyses the book titled ?Physical Conditioning for Combat Sports?, edited by Dr Emerson Franchini and Dr Tomas Herrera-Valenzuela in 2017. The book is divided in six chapters and eight authors are participating. The first chapter, ?Development of the Aerobic Capacity in Fighters?, analyses the current literature in specific training and competition situations. The second chapter, ?Development of the Anaerobic Capacity in Fighters?, describes the responses and needs of fighters in relation to anaerobic power and capacity. The third chapter, ?Maximal Strength Training in Fighters?, studies the different training methods for the specific development of this capacity. The fourth chapter, ?Development of the Muscular Power in Fighters?, details the needs of muscular power according to the different combat sports and during training and competition situations. The fifth chapter titled ?Development of the Strength Endurance in Fighters? describes the general and specific tests for fighters, including suggestions for training core muscles as well as higher and lower extremities. The sixth chapter, ?Flexibility in Combat Sports?, examines the contribution and response of this capacity in fighters from different disciplines. Finally, the extensive research experience of the authors in topics related to martial arts and combat sports together with the exhaustive and comprehensive bibliographic review carried out, give a high scientific and academic value to the book. Therefore, it is suggested to all trainers and practitioners from the different combat sports disciplines, to consult this excellent publication

Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems

We study the existence of transverse homoclinic orbits in a singular or weakly hyperbolic Hamiltonian, with $3$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The example considered consists of an integrable Hamiltonian possessing a $2$-dimensional hyperbolic invariant torus with fast frequencies $\omega/\sqrt\varepsilon$ and coincident whiskers or separatrices, plus a perturbation of order $\mu=\varepsilon^p$, giving rise to an exponentially small splitting of separatrices. We show that asymptotic estimates for the transversality of the intersections can be obtained if $\omega$ satisfies certain arithmetic properties. More precisely, we assume that $\omega$ is a quadratic vector (i.e.~the frequency ratio is a quadratic irrational number), and generalize the good arithmetic properties of the golden vector. We provide a sufficient condition on the quadratic vector $\omega$ ensuring that the Poincar\'e--Melnikov method (used for the golden vector in a previous work) can be applied to establish the existence of transverse homoclinic orbits and, in a more restrictive case, their continuation for all values of $\varepsilon\to0$

Homoclinic orbits to invariant tori in Hamiltonian systems

We consider a perturbation of an integrable Hamiltonian system which possesses invariant tori with coincident whiskers (like some rotators and a pendulum). Our goal is to measure the splitting distance between the perturbed whiskers, putting emphasis on the detection of their intersections, which give rise to homoclinic orbits to the perturbed tori. A geometric method is presented which takes into account the Lagrangian properties of the whiskers. In this way, the splitting distance is the gradient of a splitting potential. In the regular case (also known as a priori-unstable: the Lyapunov exponents of the whiskered tori remain fixed), the splitting potential is well- approximated by a Melnikov potential. This method is designed as a first step in the study of the singular case (also known as a priori-stable: the Lyapunov exponents of the whiskered tori approach to zero when the perturbation tends to zero)

Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system

We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilibrium point of a Hamiltonian system. If the frequencies of the elliptic point are nonresonant up to a certain order $K\ge4$, and a nondegeneracy condition is fulfilled, we get an estimate for the measure of the complement of the KAM tori in a neighbourhood of given radius. Moreover, if the frequencies satisfy a Diophantine condition, with exponent $\tau$, we show that in a neighbourhood of radius $r$ the measure of the complement is exponentially small in $(1/r)^{1/(\tau+1)}$. We also give a related result for quasi-Diophantine frequencies, which is more useful for practical purposes. The results are obtained by putting the system in Birkhoff normal form up to an appropiate order, and the key point relies on giving accurate bounds for its terms

Splitting and melnikov potentials in hamiltonian systems

Peer Reviewe

Evaluación de bullying y su relación con los estilos de afrontamiento utilizados por los estudiantes de las escuelas de formación de la Policía Nacional

Trabajo de investigaciónLa presente investigación es no experimental y de tipo descriptivo-correlacional, que buscó determinar sí los estudiantes de las Escuelas de Formación de la Policía Nacional perciben el fenómeno del bullying al interior del plantel e identificar los estilos de afrontamiento que suelen utilizar. Para ello, se contó con una muestra heterogénea intencionada de 211 estudiantes y se utilizó como instrumento de evaluación del bullying el INSEBULL y para evaluar estilos de afrontamiento el CAE. Los datos se analizaron con las pruebas Kolmogorov-Smirnov, suma de rangos de Wilcoxon, correlación de Pearson y análisis de contingencia. Los resultados indican que en términos generales los estudiantes de las escuelas de formación policial perciben la existencia de riesgo de verse involucrados en situaciones de bullying, demostrando que el bullying se mantiene en diferentes contextos y niveles educativos. Asimismo, se encontró que el estilo de afrontamiento que mostro mejores resultados para afrontar el riesgo de bullying es la focalización en la solución de problemas.MaestríaMagister en Psicologí

Ideación suicida, experiencias psicóticas subumbrales y síntomas depresivos: estudio de la naturaleza de sus relaciones a través del enfoque de redes en adolescentes de la provincia de Talca

98 p.Las experiencias psicóticas subumbrales (EPS) o subclínicas son comunes en población adolescente y suelen ser de carácter transitorio, aunque cuando no remiten, se asocian a mayor presencia de trastornos psiquiátricos y en algunos casos podría sospecharse de una posible etapa inicial del pródromo psicótico. La literatura indica que existe una relación entre las EPS y la ideación suicida, la que podría explicarse por factores de riesgo comunes, especialmente psicopatologías, ya que la mayoría de las personas que cometen suicidio tienen un trastorno mental diagnosticable. El objetivo del presente estudio es determinar la naturaleza de las relaciones entre las EPS, síntomas depresivos e ideación suicida durante la vida (SUICL) en población adolescente, a través de un modelo de red transdiagnóstico, que permite visualizar las relaciones complejas existentes entre experiencias tradicionalmente divididas en categorías diagnósticas, acercándose de forma más fidedigna a la presentación comórbida y heterogénea de la psicopatología. Se midieron estas variables con un instrumento de autorreporte desarrollado a partir de un set de cuestionarios (CAPE-P15, BQSPS, DASS-21 y C-SSRS). Los resultados indican que la relación entre las EPS y la ideación suicida no es específica y que se encuentra mediada por los síntomas depresivos. Por tanto, es posible concluir que la asociación entre las EPS e ideación suicida se debe a factores de riesgo comunes, entre los que se encuentran los síntomas depresivos, lo que contribuye a una mejor comprensión de los factores asociados con la ideación suicida, para la consecuente generación de formas de diagnóstico e intervención temprana. Palabras clave: Experiencias psicóticas subumbrales, ideación suicida, síntomas depresivos, enfoque de red transdiagnóstico

Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio

The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast frequency vector $\omega/\sqrt\varepsilon$, with $\omega=(1,\Omega),$ where the frequency ratio $\Omega$ is a quadratic irrational number. Applying the Poincaré--Melnikov method, we carry out a careful study of the dominant harmonics of the Melnikov potential. This allows us to provide an asymptotic estimate for the maximal splitting distance and show the existence of transverse homoclinic orbits to the whiskered tori with an asymptotic estimate for the transversality of the splitting. Both estimates are exponentially small in $\varepsilon$, with the functions in the exponents being periodic with respect to $\ln\varepsilon$, and can be explicitly constructed from the continued fraction of $\Omega$. In this way, we emphasize the strong dependence of our results on the arithmetic properties of $\Omega$. In particular, for quadratic ratios $\Omega$ with a 1-periodic or 2-periodic continued fraction (called metallic and metallic-colored ratios, respectively), we provide accurate upper and lower bounds for the splitting. The estimate for the maximal splitting distance is valid for all sufficiently small values of $\varepsilon$, and the transversality can be established for a majority of values of $\varepsilon$, excluding small intervals around some transition values where changes in the dominance of the harmonics take place, and bifurcations could occur. Read More: http://epubs.siam.org/doi/10.1137/15M1032776Peer ReviewedPostprint (published version

Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies

We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional toruswith a fast frequency vector¿/ve, with¿= (1,¿, ~¿) where ¿ is a cubic irrational number whose two conjugatesare complex, and the components of¿generate the fieldQ(¿). A paradigmatic case is the cubic golden vector,given by the (real) number ¿ satisfying ¿3= 1-¿, and ~¿ = ¿2. For such 3-dimensional frequency vectors,the standard theory of continued fractions cannot be applied, so we develop a methodology for determining thebehavior of the small divisors,k¿Z3. Applying the Poincaré-Melnikov method, this allows us tocarry outa careful study of the dominant harmonic (which depends one) of the Melnikov function, obtaining an asymptoticestimate for the maximal splitting distance, which is exponentially small ine, and valid for all sufficiently smallvalues ofe. This estimate behaves like exp{-h1(e)/e1/6}and we provide, for the first time in a system with 3frequencies, an accurate description of the (positive) functionh1(e) in the numerator of the exponent, showing thatit can be explicitly constructed from the resonance properties of the frequency vector¿, and proving that it is aquasiperiodic function (and not periodic) with respect to lne. In this way, we emphasize the strong dependence ofthe estimates for the splitting on the arithmetic properties of the frequenciesPreprin

Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies

We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a frequency vector omega = (1, Omega), where Omega is a quadratic irrational number, or a 3-dimensional torus with a frequency vector w = (1, Omega, Omega(2)), where Omega is a cubic irrational number. Applying the Poincare-Melnikov method, we find exponentially small asymptotic estimates for the maximal splitting distance between the stable and unstable manifolds associated to the invariant torus, and we show that such estimates depend strongly on the arithmetic properties of the frequencies. In the quadratic case, we use the continued fractions theory to establish a certain arithmetic property, fulfilled in 24 cases, which allows us to provide asymptotic estimates in a simple way. In the cubic case, we focus our attention to the case in which Q is the so-called cubic golden number (the real root of x(3) x - 1= 0), obtaining also asymptotic estimates. We point out the similitudes and differences between the results obtained for both the quadratic and cubic cases.Postprint (published version