Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity

We prove that, under a mild condition on the hyperbolicity of its periodic points, a map $g$ which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

Lipschitz shadowing implies structural stability

We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show that an expansive diffeomorphism having the Lipschitz shadowing property is Anosov.Comment: 11 page

Association between antiarrhythmic, electrophysiological and antioxidative effects of melatonin in ischemia/reperfusion

Melatonin is assumed to confer cardioprotective action via antioxidative properties. We evaluated the association between ventricular tachycardia and/or ventricular fibrillation (VT/VF) incidence, oxidative stress, and myocardial electrophysiological parameters in experimental ischemia/reperfusion under melatonin treatment. Melatonin was given to 28 rats (10 mg/kg/day, orally, for 7 days) and 13 animals received placebo. In the anesthetized animals, coronary occlusion was induced for 5 min followed by reperfusion with recording of unipolar electrograms from ventricular epicardium with a 64-lead array. Effects of melatonin on transmembrane potentials were studied in ventricular preparations of 7 rats in normal and ?ischemic? conditions. Melatonin treatment was associated with lower VT/VF incidence at reperfusion, shorter baseline activation times (ATs), and activation-repolarization intervals and more complete recovery of repolarization times (RTs) at reperfusion (less baseline-reperfusion difference, ΔRT) (p < 0.05). Superoxide dismutase (SOD) activity was higher in the treated animals and associated with ΔRT (p = 0.001), whereas VT/VF incidence was associated with baseline ATs (p = 0.020). In vitro, melatonin led to a more complete restoration of action potential durations and resting membrane potentials at reoxygenation (p < 0.05). Thus, the antioxidative properties of melatonin were associated with its influence on repolarization duration, whereas the melatonin-related antiarrhythmic effect was associated with its oxidative stress-independent action on ventricular activation.Fil: Sedova, Ksenia A.. Czech Technical University In Prague; República ChecaFil: Bernikova, Olesya G.. Ural Branch of Russian Academy of Sciences; RusiaFil: Cuprova, Julia I.. Czech Technical University In Prague; República ChecaFil: Ivanova, Alexandra D.. Lomonosov Moscow State University; RusiaFil: Kutaeva, Galina A.. Pitirim Sorokin Syktyvkar State University; RusiaFil: Pliss, Michael G.. Almazov National Medical Research Centre; RusiaFil: Lopatina, Ekaterina V.. University of Saint Petersburg; RusiaFil: Vaykshnorayte, Marina A.. Ural Branch Of Russian Academy Of Sciences; RusiaFil: Diez, Emiliano Raúl. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Medicina y Biología Experimental de Cuyo; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Medicas. Instituto de Fisiologia; ArgentinaFil: Azarov, Jan E.. Ural Branch of Russian Academy of Sciences; Rusia. Pitirim Sorokin Syktyvkar State University; Rusi

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

ВОЗМОЖНОСТИ ПРИМЕНЕНИЯ МЕЛАТОНИНА В ЛЕЧЕНИИ БОЛЬНЫХ С ХИРУРГИЧЕСКИМИ ЗАБОЛЕВАНИЯМИ

Since the widespread introduction of minimally invasive laparoscopic techniques in abdominal surgery there was a question - what are their physiological differences from operations withapproach by laparotomy. The study of these differences, mechanisms and their correction allows you to bring the results of operations with open approach to the laparoscopic. However, the possibility of an effective systemic exposure, allowing adapting body reaction to surgical procedures remains unresolved. To date, the use of melatonin in surgical practice is based on its functions as a neurotransmitter that can potentiate some natural protective reaction of the body. The paper analyzes the effects of melatonin, you can use as a biological adaptogenic control which generally acts as a trigger to launch a diver-seprocesses, including reparative ones in the body. The use of adaptive mechanisms initiated by melatonin in response to surgical trauma and tumor processes can be successfully applied to improve the results of surgical treatment of patients with surgical diseases operated as open and laparoscopic access.Со времени начала широкого внедрения малоинвазивных лапароскопических технологий в абдоминальной хирургии возник вопрос - в чем заключаются их физиологические отличия от операций c лапаротомным доступом. Исследование таких различий, механизмов и их коррекции позволяет приблизить результаты операций с открытым доступом к лапароскопическим. Однако возможности эффективного системного воздействия, позволяющего коррегировать реакцию организма на хирургические манипуляции, остаются неизученными. На сегодняшний день использование мелатонина в хирургической практике базируется на его функциях как нейромедиатора, способного потенциировать некоторые естественные защитные реакции организма. В работе анализируются эффекты мелатонина, позволяющие использовать его как биологический адаптогенный регулятор, который в целом выполняет роль триггера в запуске разнообразных, в том числе репаратив-ных процессов в организме. Использование адаптационных механизмов, инициируемых мелатонином в ответ на операционную травму и опухолевые процессы, может быть с успехом применено для улучшения результатов оперативного лечения пациентов с хирургическими заболеваниями оперируемых как открытым так и лапароскопическим доступом

Uniparental Genetic Heritage of Belarusians: Encounter of Rare Middle Eastern Matrilineages with a Central European Mitochondrial DNA Pool

Ethnic Belarusians make up more than 80% of the nine and half million people inhabiting the Republic of Belarus. Belarusians together with Ukrainians and Russians represent the East Slavic linguistic group, largest both in numbers and territory, inhabiting East Europe alongside Baltic-, Finno-Permic- and Turkic-speaking people. Till date, only a limited number of low resolution genetic studies have been performed on this population. Therefore, with the phylogeographic analysis of 565 Y-chromosomes and 267 mitochondrial DNAs from six well covered geographic sub-regions of Belarus we strove to complement the existing genetic profile of eastern Europeans. Our results reveal that around 80% of the paternal Belarusian gene pool is composed of R1a, I2a and N1c Y-chromosome haplogroups – a profile which is very similar to the two other eastern European populations – Ukrainians and Russians. The maternal Belarusian gene pool encompasses a full range of West Eurasian haplogroups and agrees well with the genetic structure of central-east European populations. Our data attest that latitudinal gradients characterize the variation of the uniparentally transmitted gene pools of modern Belarusians. In particular, the Y-chromosome reflects movements of people in central-east Europe, starting probably as early as the beginning of the Holocene. Furthermore, the matrilineal legacy of Belarusians retains two rare mitochondrial DNA haplogroups, N1a3 and N3, whose phylogeographies were explored in detail after de novo sequencing of 20 and 13 complete mitogenomes, respectively, from all over Eurasia. Our phylogeographic analyses reveal that two mitochondrial DNA lineages, N3 and N1a3, both of Middle Eastern origin, might mark distinct events of matrilineal gene flow to Europe: during the mid-Holocene period and around the Pleistocene-Holocene transition, respectively

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered