caa a22 4500 445836679 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0761-y doi (NATIONALLICENCE)springer-10.1007/s00209-010-0761-y Mihailescu Eugen Institute of Mathematics "Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania aut Unstable directions and fractal dimension for skew products with overlaps in fibers [Elektronische Daten] [Eugen Mihailescu] A unique feature of smooth hyperbolic non-invertible maps is that of having different unstable directions corresponding to different prehistories of the same point. In this paper we construct a new class of examples of non-invertible hyperbolic skew products with thick fibers for which we prove that there exist uncountably many points in the locally maximal invariant set Λ (actually a Cantor set in each fiber), having different unstable directions corresponding to different prehistories; also we estimate the angle between such unstable directions. We discuss then the Hausdorff dimension of the fibers of Λ for these maps by employing the thickness of Cantor sets, the inverse pressure, and also by use of continuous bounds for the preimage counting function. We prove that in certain examples, there are uncountably many points in Λ with two preimages belonging to Λ, as well as uncountably many points having only one preimage in Λ. In the end we give examples which, also from the point of view of Hausdorff dimension, are far from being homeomorphisms on Λ, as well as far from being constant-to-1 maps on Λ. Springer-Verlag, 2010 Chaotic dynamics of hyperbolic non-invertible skew products nationallicence Cantor sets nationallicence Unstable manifolds for smooth endomorphisms nationallicence Hausdorff dimension of fractals nationallicence Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 733-750 0025-5874 269:3-4<733 2011 269 209 https://doi.org/10.1007/s00209-010-0761-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0761-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mihailescu Eugen Institute of Mathematics "Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 733-750 0025-5874 269:3-4<733 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer