104 research outputs found
A quasiperiodically forced skew-product on the cylinder without fixed-curves
In [FJJK] the Sharkovski\u{i} Theorem was extended to periodic orbits of
strips of quasiperiodic skew products in the cylinder. In this paper we deal
with the following natural question that arises in this setting: Does
Sharkovski\u{i} Theorem holds when restricted to curves instead of general
strips?mWe answer this question in the negative by constructing a
counterexample: We construct a map having a periodic orbit of period 2 of
curves (which is, in fact, the upper and lower circles of the cylinder) and
without any invariant curve. In particular this shows that there exist
quasiperiodic skew products in the cylinder without invariant curves
Sistemes dinámics : les matemà tiques del professor W. Szlenk
L'objectiu d'aquesta xerrada Ă©s donar a conèixer a nivell humĂ i matemĂ tic la figura d'en WiesĹ‚aw Szlenk, mort el 26 de juliol de 1995 a l'Hospital ClĂnic de Barcelona, a aquells membres de la comunitat matemĂ tica de la Universitat Autònoma de Barcelona que no hi varen tenir un contacte intens
Semiconjugacy to a map of a constant slope
It is well known that a continuous piecewise monotone interval map with
positive topological entropy is semiconjugate to a map of a constant slope and
the same entropy, and if it is additionally transitive then this semiconjugacy
is actually a conjugacy. We generalize this result to piecewise continuous
piecewise monotone interval maps, and as a consequence, get it also for
piecewise monotone graph maps. We show that assigning to a continuous
transitive piecewise monotone map of positive entropy a map of constant slope
conjugate to it defines an operator, and show that this operator is not
continuous
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