We consider a fixed point free homeomorphism of the closed band which leaves each leaf of a Reeb foliation on invariant. Assuming is the time one of various topological flows, we compare the restriction of the flows on the boundary.
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.
La fonction de récurrence d’une suite symbolique compte au bout de combien de temps on voit tous les mots de longueur . Nous la calculons explicitement pour les suites d’Arnoux-Rauzy, définies par des conditions combinatoires qui en font une généralisation naturelle des suites sturmiennes. Puis nous répondons à une question de Morse et Hedlund (1940) en montrant que ne peut avoir une limite finie pour aucune suite non ultimement périodique.
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
Let be the tent map with slope a. Let c be its turning point, and the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.
We consider-without restriction to the piecewise monotone case-a forcing relation on interval (transitive, roof, bottom) patterns. We prove some basic properties of this type of forcing and explain when it is a partial ordering. Finally, we show how our approach relates to the results known from the literature.
Let ℳ be the set of pairs (T,g) such that T ⊂ ℝ is compact, g: T → T is continuous, g is minimal on T and has a piecewise monotone extension to convT. Two pairs (T,g),(S,f) from ℳ are equivalent if the map h: orb(minT,g) → orb(minS,f) defined for each m ∈ ℕ₀ by is increasing on orb(minT,g). An equivalence class of this relation-a minimal (oriented) pattern A-is exhibited by a continuous interval map f:I → I if there is a set T ⊂ I such that (T,f|T) = (T,f) ∈ A. We define the forcing relation on...