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Kleine Nenner: Zahlentheorie in dynamischen Systemen

In: Eine Einladung in die Mathematik

Author

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  • Jean-Christophe Yoccoz

    (Collège de France)

Abstract

Zusammenfassung Wir untersuchen dynamische Systeme mit zwei oder mehr sich bewegenden Teilchen, wie etwa zwei Planeten, die um die Sonne kreisen. Wenn das Verhältnis α der beiden Rotationsperioden rational ist, befinden sich die Planeten in Resonanz, und die paarweise Wechselwirkung führt zu instabiler Dynamik. Wenn das Periodenverhältnis α irrational ist, kann es beliebig gut durch rationale Zahlen angenähert werden, und die Stabilität hängt davon ab, wie gut diese Näherung abhängig von den Größenihrer Zähler und Nenner ist.

Suggested Citation

  • Jean-Christophe Yoccoz, 2013. "Kleine Nenner: Zahlentheorie in dynamischen Systemen," Springer Books, in: Dierk Schleicher & Malte Lackmann (ed.), Eine Einladung in die Mathematik, edition 127, pages 43-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25798-8_4
    DOI: 10.1007/978-3-642-25798-8_4
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