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    Wyświetlanie 1-6 z 6
    Tytuł:
    Relatively minimal extensions of topological flows
    Autorzy:
    Mentzen, Mieczysław
    Powiązania:
    https://bibliotekanauki.pl/articles/965711.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    factors
    flows
    topological dynamics
    Opis:
    The concept of relatively minimal (rel. min.) extensions of topological flows is introduced. Several generalizations of properties of minimal extensions are shown. In particular the following extensions are rel. min.: distal point transitive, inverse limits of rel. min., superpositions of rel. min. Any proximal extension of a flow Y with a dense set of almost periodic (a.p.) points contains a unique subflow which is a relatively minimal extension of Y. All proximal and distal factors of a point transitive flow with a dense set of a.p. points are rel. min. In the class of point transitive flows with a dense set of a.p. points, distal open extensions are disjoint from all proximal extensions. An example of a relatively minimal point transitive extension determined by a cocycle which is a coboundary in the measure-theoretic sense is given.
    Źródło:
    Colloquium Mathematicum; 2000, 84/85, 1; 51-65
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some families of pseudo-processes
    Autorzy:
    Kłapyta, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1311655.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    topological dynamics
    dispersiveness
    unstability
    stability
    Opis:
    We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space $ℝ^m$. The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.
    Źródło:
    Annales Polonici Mathematici; 1994-1995, 60, 1; 33-45
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Chaos theory from the mathematical point of view
    Autorzy:
    Kwietniak, Dominik
    Oprocha, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/748392.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    topological dynamics, chaos, topological entropy, topological transitivity, topological horseshoe, Li-Yorke chaos, Auslander-Yorke chaos, Devaney chaos, distributional chaos, Li-Yorke pair, sensitivity.
    Opis:
    Niniejsza praca stanowi próbę przedstawienia istniejących definicji chaosu dla dyskretnych układów dynamicznych. Dyskusję zawężono do zagadnień związanych z dynamiką topologiczną. Przedstawiono i umotywowano definicje: wrażliwości na warunki początkowe, chaosu w sensie Li i Yorke’a, Auslandera i Yorke’a, Devaneya, chaosu dystrybucyjnego, entropii topologicznej i podkowy topologicznej. Podzielono się pewnymi uwagami historycznymi. Omówiono znane związki między różnymi definicjami chaosu i przypomniano związane z nimi problemy otwarte.
    This work is intended as an attempt to survey existingde finitions of chaos for discrete dynamical systems. Discussion is restricted to the settingof topological dynamics, while the measure-theoretic (ergodic theory) and smooth (differentiable dynamical systems) aspects are omitted as exceedingt he scope of this paper. Chaos theory is understood here as a part of topological dynamics, so aforementioned definitions of chaos are just examples of particular dynamical system properties, and are considered inside the framework of the mathematical theory of discrete dynamical systems. It is not the purpose of this article to study chaos theory understood as a new kind of interdisciplinary branch of science devoted to nonlinear phenomena. As for prerequisites, the reader is expected to possess some mathematical maturity, and to be familiar with basic topology of (compact) metric spaces. No preliminary knowledge of the dynamical systems theory is required, however some is recommended. The first two section are devoted to general discussion of the term „chaos” and contains authors opinion on this subject. To facilitate access to the rest of the article some relevant material from the dynamical system theory is briefly repeated in the third section. The next section (Section 4) introduces the notion of topological transitivity along with some stronger variants, namely topological mixing and weak mixing. Section 5 gives a detailed account of the famous Sharkovskii’s Theorem in its full generality. This is required for characterization of chaotic interval maps. Sections 6-13 are devoted to various notions of chaos or related to chaos in dynamical systems. Each section contains an attempt to motivate the notion, historical background and formal definition followed with a review of known properties, relations between various notions of chaos, and some relevant open problems. Section 6 is devoted to a sensitivity to initial conditions – a notion which is accepted as a basic indicator of chaotic behavior. Section 7 introduces a definition of chaos accordingt o Auslander and Yorke. Section 8 examines the notion of Li-Yorke pair and Li-Yorke chaos. Section 9 deals with the definition of chaos introduced in Devaney’s book (Devaney chaos). Section 10 recalls some facts connected with symbolic dynamics, which provides a rich source of examples for various interestingb ehavior, and it is an indispensable tool for exploration of many systems. Section 11 describes the so-called “topological horseshoes”, which are generalizations of the famous example due to Smale. The existence of a horseshoe in a given dynamical system proves the existence of a subsystem with a dynamics similar to some symbolic dynamical system, hence with a very complicated behavior. Section 12 gives a brief exposition of the topological entropy and its relation to chaos. The review of various notions of chaos ends with section 13, containingd escription of distributional chaos.
    Źródło:
    Mathematica Applicanda; 2008, 36, 50/09
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time weighted entropies
    Autorzy:
    Schmeling, Jörg
    Powiązania:
    https://bibliotekanauki.pl/articles/965770.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    topological entropy
    symbolic dynamics
    Opis:
    For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.
    Źródło:
    Colloquium Mathematicum; 2000, 84/85, 1; 265-278
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Chaotic dynamics in the Volterra predator-prey model via linked twist maps
    Autorzy:
    Pireddu, M.
    Zanolin, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255348.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Volterra predator-prey system
    harvesting
    periodic solutions
    subharmonics
    chaotic-like dynamics
    topological horseshoes
    linked twist maps
    Opis:
    We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator-prey model with a periodic harvesting. The proof relies on some recent results about chaotic planar maps combined with the study of geometric features which are typical of linked twist maps.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 567-592
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new tool for topological optimization of a rotor for vertical axis wind turbines
    Autorzy:
    Jakubowski, M.
    Fritzkowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/127945.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Poznańska. Instytut Mechaniki Stosowanej
    Tematy:
    vertical axis wind turbine
    topological optimization
    computational fluid dynamics
    turbiny wiatrowe o pionowej osi obrotu
    optymalizacja topologiczna
    obliczeniowa dynamika płynów
    Opis:
    A computer program for topological optimization of a rotor for vertical axis wind turbines of various type is presented. The tool is based mainly on two external modules: the GMSH mesh generator and the OpenFOAM CFD toolbox. Interpolation of rotor blades geometry and computational model of the airflow through a turbine are briefly discussed. Moreover, a simple optimization algorithm is described. Exemplary results for a H-type rotor are presented. Finally, potential directions for the software development are indicated.
    Źródło:
    Vibrations in Physical Systems; 2016, 27; 143-150
    0860-6897
    Pojawia się w:
    Vibrations in Physical Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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