Michal Misiurewicz

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We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z e C: z3 e [0,1]} into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into(More)
© Publications mathématiques de l’I.H.É.S., 1981, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression(More)
© Publications mathématiques de l’I.H.É.S., 1981, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression(More)
For a family of dynamical systems we define sensitive dependence on parameters in a way resembling Guckenheimer’s definition of sensitive dependence on initial conditions. While sensitive dependence on initial conditions tells us that if we know the initial condition only approximately then we cannot make deterministic predictions, sensitive dependence on(More)
The same holds for continuous maps of the real line into itself, except that we may have P (f) = ∅. All proofs of Sharkovsky’s Theorem inevitably lead to an idea of a “type” of a cycle. For instance, when ordering the points of a cycle p1 < p2 < · · · < pn, one gets a cyclic permutation σ corresponding to it, such that pi is mapped to pσ(i). Combinatorial(More)