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Geometry of geometrically finite one-dimensional maps

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Abstract

We study the geometry of certain one-dimensional maps as dynamical systems. We prove the property of bounded and bounded nearby geometry of certainC 1+α one-dimensional maps with finitely many critical points. This property enables us to give the quasisymmetric classification of geometrically finite one-dimensional maps.

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References

  1. Ahlfors, L.A.: Lectures on quasiformal maps. D. von Nostrand 1966

  2. Bieberbach, L.: Conformal mapping. New York: Chelsea Publishing 1953

    Google Scholar 

  3. Cawley, E.: The Teichmüller space of an Anosov diffeomorphism ofT 2. IMS preprint series 1991/8, SUNY at Stony Brook

  4. Jiang, Y.: Leading gap determine the geometry of Cantor set. Preprint 1988, Graduate Center of CUNY and IHES preprint June 1989

  5. Jiang, Y.: Generalized Ulam-von Neumann transformation. Thesis, 1990, Graduate Center of CUNY

  6. Jiang, Y.: Dynamics of certain smooth one-dimensional maps. I. TheC 1+α-Denjoy-Koebe distortion lemma and II. Geometrically finite one-dimensional maps. IMS preprint series 1991/1, SUNY at Stony Brook

  7. Jiang, Y.: On quasisymmetrical classification of infinitely renormalizable maps, I. Maps with the Feigenbaum's topology and II. Remarks on maps with a bounded type topology. IMS preprint series 1992/19, SUNY at Stony Brook

  8. Milnor, J., Thurston, W.: On iterated maps of the interval I and II. Preprint, 1977, Princeton University

  9. Sullivan, D.: Seminar on conformal and hyperbolic geometry. IHES preprint, March 1982

  10. Sullivan, D.: Class notes, 1987

  11. Sullivan, D.: Bounds, quadratic differentials, and renormalization conjectures. Providence, RI: American Mathematical Society Centennian Publications, Volume 2: Mathematics into the Twenty-first Century

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Authors and Affiliations

  1. Department of Mathematics, Queens College of CUNY, 65-30 Kissena Blvd, 11367, Flushing, NY, USA

    Yunping Jiang

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  1. Yunping Jiang
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Communicated by S.-T. Yau

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Jiang, Y. Geometry of geometrically finite one-dimensional maps. Commun.Math. Phys. 156, 639–647 (1993). https://doi.org/10.1007/BF02096866

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  • DOI: https://doi.org/10.1007/BF02096866

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