Displaying similar documents to “On fixed points of C 1 extensions of expanding maps in the unit disc”

Invariant densities for C¹ maps

Anthony Quas (1996)

Studia Mathematica

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We consider the set of C 1 expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of C 1 expanding maps with the C 1 topology. This is in contrast with results for C 2 or C 1 + ε maps, where the invariant densities can be shown to be continuous.

Most expanding maps have no absolutely continuous invariant measure

Anthony Quas (1999)

Studia Mathematica

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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic C 1 expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for C 2 or C 1 + ε expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.

A characterization of the kneading pair for bimodal degree one circle maps

Lluis Alsedà, Antonio Falcó (1997)

Annales de l'institut Fourier

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For continuous maps on the interval with finitely many monotonicity intervals, the kneading theory developed by Milnor and Thurston gives a symbolic description of the dynamics of a given map. This description is given in terms of the kneading invariants which essentially consists in the symbolic orbits of the turning points of the map under consideration. Moreover, this theory also describes a classification of all such maps through theses invariants. For continuous bimodal degree one...

Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms

S. Siboni (1998)

Bollettino dell'Unione Matematica Italiana

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Viene considerata una classe di sistemi dinamici del toro bidimensionale T 2 . Tali sistemi presentano la forma di un prodotto skew fra l'endomorfismo Bernoulli B p ⁢ x = mod ⁡ p ⁢ x , 1 , p ∈ Z ∖ - 1 , 0 , 1 , definito sul toro undidimensionale T 1 ≡ 0 , 1 ed una traslazione del toro stesso. Si dimostra che gli esponenti di Liapunov e l'entropia di Kolmogorov-Sinai della misura di Haar invariante possono essere calcolati esplicitamente. Viene infine discusso il decadimento delle correlazioni per i caratteri.