Research publications and Preprints
- Low-dimensional analytic dynamics (rigidity and small divisors)
- Geometric analysis (quasi-conformal mappings and elliptic PDEs)
- Renormalization operators (on infinite dimensional spaces)
Manuscripts in preparation
- Hairy Cantor sets,
40 pages, preprint 2019.
- 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
- Complex Feigenbaum phenomena of high type, (with M. Pedramfar)
- Dimension paradox of irrationally 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,
Selected slides of talks
- 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.
Gallery of dynamically generated pictures
- 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