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Displaying similar documents to “Solvability Of Operator Equations And Periodic Solutions Of Semilinear Hyperbolic Equations”

C¹-maps having hyperbolic periodic points

N. Aoki, Kazumine Moriyasu, N. Sumi (2001)

Fundamenta Mathematicae

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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.

Trees of visible components in the Mandelbrot set

Virpi Kauko (2000)

Fundamenta Mathematicae

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We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

Remarks on the relative intrinsic pseudo-distance and hyperbolic imbeddability

Nguyen Doan Tuan, Pham Viet Duc (2005)

Annales Polonici Mathematici

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We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.