Displaying similar documents to “Common fixed point theorems for compatible self-maps of Hausdorff topological spaces.”

On the primary orbits of star maps (first part)

Lluis Alsedà, Jose Miguel Moreno (2002)

Applicationes Mathematicae

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This paper is the first one of a series of two, in which we characterize a class of primary orbits of self maps of the 4-star with the branching point fixed. This class of orbits plays, for such maps, the same role as the directed primary orbits of self maps of the 3-star with the branching point fixed. Some of the primary orbits (namely, those having at most one coloured arrow) are characterized at once for the general case of n-star maps.

On the primary orbits of star maps (second part: spiral orbits)

Lluís Alsedà, José Miguel Moreno (2002)

Applicationes Mathematicae

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This paper is the second part of [2] and is devoted to the study of the spiral orbits of self maps of the 4-star with the branching point fixed, completing the characterization of the strongly directed primary orbits for such maps.

Periodic orbits and chain-transitive sets of C1-diffeomorphisms

Sylvain Crovisier (2006)

Publications Mathématiques de l'IHÉS

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We prove that the chain-transitive sets of C-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...