Institute for Mathematical Science
Stony Brook University

office: Math Tower 4-103
phone: (631) 632-8266

## Synopsis

My interests are in the areas of complex dynamics (in one or several variables), analysis, topology and the interplay between these fields. My research is focused on the study of complex Hénon maps, which are a special class of polynomial automorphisms of $\mathbb{C}^2$ with chaotic behavior. I am interested in understanding the global topology of the Julia sets $J$, $J^-$ and $J^+$ of a complex Hénon map. I am also interested in understanding the dynamics of maps with non-hyperbolic behavior such as Hénon maps or more generally holomorphic germs of $(\mathbb{C}^2,0)$ with a semi-indifferent fixed point. Some specific topics that I work on include: relative stability of semi-parabolic Hénon maps and connectivity of the Julia set $J$, regularity properties of the boundary of a Siegel disk of a semi-Siegel Hénon map, local structure of a non-linearizable germ of $(\mathbb{C}^2,0)$ with irrational rotation number.

## Papers and preprints

• R. Radu, R. Tanase, Semi-parabolic tools for hyperbolic Hénon maps and continuity of Julia sets in $\mathbb{C}^2$,
arXiv:1508.03625, to appear in Transactions of the AMS
• R. Radu, R. Tanase, A structure theorem for semi-parabolic Hénon maps, arXiv:1411.3824, Submitted
• R. Radu, R. Tanase, A new proof of a theorem of Hubbard and Oberste-Vorth, Fixed Point Theory
and Applications, (2016) 2016:43, arXiv:1511.03256
• D. Gaidashev, R. Radu, M. Yampolsky, Renormalization and Siegel disks for complex Hénon maps,
arXiv:1604.07069
• M. Lyubich, R. Radu, R. Tanase, Hedgehogs in higher dimensions and their applications, arXiv:1611.09840
• T. Firsova, M. Lyubich, R. Radu, R. Tanase, Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of $(\mathbb{C}^2,0)$, arXiv:1611.09342
• R. Radu, A global model for the Julia set $J^+$, Preprint 2016
• S. Bonnot, R. Radu, R. Tanase, Hénon maps with biholomorphic escaping sets, In preparation

## Thesis

R. Radu, Topological models for hyperbolic and semi-parabolic complex Hénon maps, Cornell University, 2013

## Selected talks and slides

• JMM-AMS Special Session on Ergodic Theory and Dynamical Systems, Atlanta, January 4-7, 2017
• New Trends in One-dimensional Dynamics, celebrating the 70th birthday of Welington de Melo, IMPA, Rio de Janeiro, November 14-18, 2016
• Dynamics Seminar, University of Uppsala, October 11, 2016
• Dynamics Seminar, University of Chicago, April 11, 2016
• Special session on Holomorphic Dynamics, AMS Sectional Meeting, Stony Brook, March 18-20, 2016
• 50th Spring Topology and Dynamical Systems Conference, Special Session in Dynamical Systems, Baylor University, TX, March 9-13, 2016
• Dynamics Seminar, University of Michigan, October 26, 2015
• Dynamics Seminar, University of Toronto, September 28, 2015
• Dynamical Developments: a conference in Complex Dynamics and Teichmuller theory, in honor of the 70th birthday of John Hubbard, Bremen, Germany, August 17-20, 2015
• International Congress of Romanian Mathematicians, special session on "Dynamics and Ergodic Theory", Iasi, Romania, June 26 - July 1, 2015
• Dynamics Seminar, Cornell University, April 17, 2015
• Dynamics Seminar, An Afternoon on Hénon Dynamical Systems, Imperial College London, March 12, 2015
• The International Congress of Mathematicians (ICM), special session on "Dynamical Systems and Ordinary Differential Equations", short communication, Seoul, South Korea, August 13-21, 2014
• Sixth Iberoamerican Congress on Geometry, CUNY, May 20-24, 2014
• CMS Winter Meeting, special session on "Holomorphic Dynamics and Related Topics", Ottawa, Canada, December 6-8, 2013
• Joint International Meeting of the American Mathematical Society (AMS) and the Romanian Mathematical Society (RMS), special session on "Complex Geometry and Dynamics", Alba Iulia, Romania, June 27-30, 2013
• Seminário de Sistemas Dinâmicos, University of São Paulo, Brazil, October 3, 2012
• Interactions between continuous and discrete holomorphic dynamical systems, Banff, Canada, July 8-13, 2012
• Analysis Seminar, Cornell University, February 13, 2011

Last updated December 2016