Title
Selecta Mathematica Iv: Einige Grundbegriffe Der Topologischen Dynamik. Poincares Wiederkehrsatz. Gleichverteilung Mod 1. Markov,Used
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Von jeher haben vViederkehrerscheinungen das Interesse nachdenk licher Leute gefunden und insbesondere mathematische Untersuchungen angeregt. Periodisches Zahlen verbinden wir mit der Regelmassigkeit eines Rhythmus, Translationsgruppen mit der Wiederkehr in Fries mustern, und die Umlaufe der Planeten verlangten Newton die Erfin dung der Infinitesimalrechnung ab. Es geht aber nicht nur darum, beobachtete Wiederkehr in mathematischen Modellen nachzuzeichnen, sondern auch um die grundsatzliche Frage: Warum muss Wiederkehr sein? Genauer: Welche Eigenschaften eines mathematischen Modells erzwingen das Auftreten von Wiederkehrerscheinungen ? Die Antwort der Mathematik auf diese Frage sind die sog. vVieder kehrsatze, von denen wir die wichtigsten in diesem Band in typischer Gestalt, wenn auch nicht immer in grosstmoglicher Allgemeinheit vor stellen. Sie lassen sich nach der Art der zugrunde gelegten Strukturen unterscheiden. Arbeitet man mit rein topologischen Mitteln, so befindet man sich in der sog. topologischen Dynamik, der unser erster Beitrag gilt. Der hier bewiesene Wiederkehrsatz 3.9 stutzt sich vor allem auf die Kom paktheit des zugrunde liegenden Raums und zeigt die Existenz fast periodischer Bewegungen. Starre Bewegungen eines speziellen Kompaktums, namlich der Kreislinie (oder allgemeiner: eines Torus), sowie einen strengeren Fast periodizitatsbegriff untersucht der zweite Beitrag uber Gleichverteilung mod 1, in dem wir Weyls beruhmten Satz beweisen, und den Leser auch etwas in die Mittelwerttheorie der fastperioiischen Funktionen ein fuhren.'
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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