Department of Mathematics

Uppsala University

Uppsal, Sweden

I am currently a member of the Department of Mathematics at Uppsala University. I did my undergraduate studies at MEPhI , and the graduate ones at University of Texas at Austin, my frist postdoc at University of Toronto in Toronto, and the second one at KTH in Stockholm.

Mainly dynamical systems, a little bit of solitonistics, non-linear evolution PDE's, and similar beasts... Here's my CV .

I am a co-organizer of the joint KTH-UU "Dynamics, Number theory and Analysis (DNA) seminar". For the seminar schedule please visit the DNA page .

Applied Dynamical Systems, 1MA444, Fall 2018 Ordinary Differential Equations II, 1MA208, Spring 2018 Dynamical Systems, 1MA217, Fall 2016 Applied Dynamical Systems, 1MA151, Fall 2015 Fourieranalys, 1MA211, Fall 2013 Partial Differential Equations, 1MA216, Fall 2013 Dynamical Systems, 1MA217, Fall 2012

- Renormalization of non-twist Hamiltonian flows, program package
- Transverse instability of a 2-D Benjamin-Ono equation, program package
- A Beltrami solver, program package
- A Beltrami solver with rigorous bounds for the cylinder renormalization problem, program package
- Cylinder renormaliation for Siegel disks, program package
- Period doubling in area-preserving maps, hyperbolic and stable sets, program package
- Perturbations of the Feigenbaum equation, program package
- Analyticity and compactness of renormlization via mild computer assistence, program package
- Spectral properties of period doubling renormalization for area-preserving maps, program package

- Existence of stochastic parameters in Henon-like families with definite dissipation, preprint
- Renormalization and Siegel disks for complex Henon maps, with Michael Yampolsky and Remus Radu, e-print math/DS:1604.07069
- Renormalization for almost commuting pairs, with Michael Yampolsky, e-print math/DS:1604.00719
- Golden mean Siegel disk universality and renormalization, with Michael Yampolsky, e-print math/DS:1604.00717
- Spectral properties of the renormalization for area-preserving maps, preprint, with Tomas Johnson,
*Discrete Contin. Dyn. Sys.*A 36(7) (2016) - Rigidity for infinitely renormalizable area-preserving maps, with Tomas Johnson and Marco Martens,
*Duke Math. J.*165(1) (2016) - Renormalization for Lorenz maps of monotone combinatorial types , submitted, e-print math/DS:1204.2504
- On the scaling ratios for Siegel disks
*Comm. Math. Phys.*333(2) (2015) - Existence of a Lorenz renormalization fixed point of an arbitrary critical order, with Björn Winckler,
*Nonlinearity*, 25 (2012), p 1819 - A Numerical Study of Infinitely Renormalizable Area-preserving Maps, with Tomas Johnson,
*Dynamical Systems*, 27(3) (2012), 283-301 - Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistence in Contraction Mapping Principle,
*Int. Journal of Bifurcations and Chaos*, 21(11) (2011) - Period doubling in area-preserving maps: an associated one-dimensional problem,
*Erg. Theory and Dyn. Sys.*31(4) (2011), 1193-1228 - On analytic perturbations of a family of Feigenbaum-like equations,
*J. Math. Anal. and Appl.*374(2) (2010), 355-373. - Dynamics of the Universal Area-Preserving Map Associated with Period
Doubling: Stable Sets, with Tomas Johnson,
*J. Mod. Dyn.*3(4) (2009), 1-39 - Dynamics of the Universal Area-Preserving Map Associated with
Period Doubling: Hyperbolic Sets, with Tomas Johnson,
*Nonlinearity*22(10) (2009), 2487-2521. - On numerical algorithms for the solution of a Beltrami equation , with Dima
Khmelev,
*SIAM J Numer Analysis*46(5) (2008), 2238-2253. - Cylinder renormalization for Siegel disks, with Michael Yampolsky,
*Exp. Math.*16(2) (2007), 215-226. - Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem ,
*Nonlinearity*20(3) (2007), 713-741. - Renormalization of isoenergetically degenerate Hamiltonian flows and associated bifurcations of invariant
tori,
*Discrete Contin. Dyn. Syst*13(1) (2005), 63-102 - Renormalization and shearless invariant tori: numerical results, with Hans
Koch,
*Nonlinearity*17(5) (2004), 1713-1722. - On the transverse instability of the 2-D Benjamin-Ono solitons, with Sergey Zhdanov,
*Phys. Fluids*16(6) (2004), 1915-1921.