Dr Davoud Cheraghi


Davoud Cheraghi


Research Interests

  • Low-dimensional analytic dynamics (rigidity and small divisors)
  • Geometric analysis (quasi-conformal mappings and elliptic PDEs)
  • Renormalization operators (on infinite dimensional spaces)
Research publications and Preprints
  • Toplogy of irrationally indifferent attractors,
    52 pages, preprint 2017.
  • Satellite renormalization of quadratic polynomials, (with M. Shishikura),
    71 pages, preprint 2015.
  • Statistical properties of quadratic polynomials with a neutral fixed point, (with A. Avila)
    Journal of the European Mathematical Society, Volume 20, Issue 8, 2018, (57 pages), preprint
  • Typical orbits of quadratic polynomials with a neutral fixed point: Non-Brjuno type
    Ann. Sci. 'Ecole Norm. Sup., in Press 2017, (82 pages), preprint
  • A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type, (with A. Cheritat)
    Invent. Math. 202 (2015), no. 2, 677–742, (66 pages), preprint
  • Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
    Commun. Math. Phys. 322 (2013), no. 3, 999-1035, (37 pages), preprint
  • Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
    Conform. Geom. Dyn. 14 (2010), 219-255, (37 pages), preprint
Manuscripts in preparation
  • Complex Feigenbaum phenomena of high type, (with M. Pedramfar)
  • Dimension paradox of irrationall indifferent attractors (with A. De Zotti and F. Yang)
  • Topology of isentropes in a two parameter family of unimodal maps, (with S. van Strien)
  • Combinatorial-analytic multipliers and the asymptotic geometry of the Mandelbrot set,
  • Measurable dynamics of holomorphic maps with a nonlinearizable fixed point,
Other
  • Chapter on dynamical systems in the book Mathematics of Planet earth, a primer, World Scientific, 2017.
  • One dimensioanl real and complex dynamics, lecture notes of the TCC course, 52 pages, Spring 2014.
  • Geometric complex analysis, lecture notes , 98 pages, Autumn 2016.
  • Analytic number theory, lecture notes , 66 pages, Winter 2016.
  • Dynamics of complex unicritical polynomials, PhD thesis (150 pages), Sept 2009.
  • Measurable dynamics of geodesic flow on rank one Riemannian manifolds, MSc thesis (a survey in Farsi, 109 pages), 2004.
Selected slides of talks
  • Satellite renormalization of quadratic polynomials, slides of the the first two lectures of an eight-lecture minicourse at the Simon's semeter at Banach center in Warsaw, September 2015.
  • Typical orbits of quadratic polynomials with a neutral fixed point, slides at Seillac, France, May 2010, and a longer one, slides, at University of Liverpool, Apr 2010.
  • Attractors of quadratic polynomials with an irrationally indifferent fixed point, slides at National University of Singapore, 2012.
  • Combinatorial rigidity of infinitely renormalizable unicritical polynomials, slides at Roskilde University in Copenhagen, Sept 2010
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