Dr Davoud Cheraghi

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Curriculum Vitae
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Research Interests

• Low-dimensional analytic dynamics (rigidity and small divisors)
• Geometric analysis (quasi-conformal mappings and elliptic PDEs)
• Renormalization operators (on infinite dimensional spaces)

Publications and Preprints

• Cubic Siegel polynomials and the bifurcation measure
  Matthieu Astorg, D. Cheraghi, Arnaud Cheritat
  arxiv.org/abs/2410.20179, 2024.
• Arithmetic geometric model for the renormalisation of irrationally indifferent attractors
  D. Cheraghi
  Nonlinearity 36 (2023), no. 12, 6403-6475.
• Lacunary series, resonances, and automorphisms of ℂ² with a round Siegel domain
  Francois Berteloot, D. Cheraghi
  Kyoto J. Math. 63 (2023), no.2, 421-433.
• Hairy Cantor sets
  D. Cheraghi, Mohammad Pedramfar
  Adv. Math. 398, 2022,
• Analytic maps of parabolic and elliptic type with trivial centralisers
  Artur Avila, D. Cheraghi, Alexander Eliad
  Ann. Inst. H. Poincare Anal. Non Lineaire, Vol 39, No 4, 2022.
• Dimension paradox of irrationally indifferent attractors
  D. Cheraghi, Alexandre De Zotti, Fei Yang
  arXiv:2003.12340, 2020.
• Typical orbits of quadratic polynomials with a neutral fixed point: Non-Brjuno type
  D. Cheraghi
  Ann. Sci. 'Ecole Norm. Sup., Vol 1 (52), pp. 59-138, 2019.
• Statistical properties of quadratic polynomials with a neutral fixed point
  Artur Avila, D. Cheraghi
  J. Eur. Math. Soc. (JEMS), Volume 20, Issue 8, pp. 2005-2062, 2018.
• Topology of irrationally indifferent attractors
  D. Cheraghi
  arxiv:1706.02678, 58 pages, 2017.
• Mathematics of Planet Earth, a primer
  J. Brocker, B. Calderhead, D. Cheraghi, C. Cotter, D. Holm, T. Kuna, B. Pelloni, T. Shepherd, H. Weller
  Advanced Textbooks in Mathematics, World Scientific, 372 pages, 2017.
• Satellite renormalization of quadratic polynomials
  D. Cheraghi, Mitsuhiro Shishikura
  arxiv:1509.07843, 2015.
• A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
  D. Cheraghi, Arnaud Cheritat
  Invent. Math. 202, no. 2, pp. 677-742, 2015.
• Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
  D. Cheraghi
  Commun. Math. Phys. 322, no. 3, pp. 999-1035, 2013.
• Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
  D. Cheraghi
  Conform. Geom. Dyn. 14, pp. 219-255, 2010.

Manuscripts in preparation

• Complex Feigenbaum phenomena of high type, (with M. Pedramfar)
• 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,

Lecture notes

• 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.

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

Gallery of dynamically generated pictures

• The Siegel disks of quadratic polynomials