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Displaying similar documents to “On the orbit of the centralizer of a matrix”

Podal subspaces on the unit polydisk

Kunyu Guo (2002)

Studia Mathematica

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Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points....

Orbits connecting singular points in the plane

Changming Ding (2005)

Czechoslovak Mathematical Journal

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This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed. ...

Existence and construction of two-dimensional invariant subspaces for pairs of rotations

Ernst Dieterich (2009)

Colloquium Mathematicae

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By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove...

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...