## Anton Gorodetski

Assistant Professor, Mathematics

School of Physical Sciences

School of Physical Sciences

Ph.D., Moscow State University, 2001, Mathematics

University of California, Irvine

510G Rowland Hall

Mail Code: 3875

Irvine, CA 92697

510G Rowland Hall

Mail Code: 3875

Irvine, CA 92697

**Research Interests**

Dynamical systems

**Appointments**

Independent University of Moscow, Russia, 2001-2003

Moscow State University, Russia, 2001-2003

Caltech, 2003-2007

Moscow State University, Russia, 2001-2003

Caltech, 2003-2007

**Research Abstract**

My research interests are mostly in the field of smooth dynamical systems, including

-partially hyperbolic and non-uniformly hyperbolic dynamics;

-nonlocal and homoclinic bifurcations;

-structure of Newhouse domains (in both dissipative and conservative setting);

-applications to problems in other fields of mathematics (including celestial mechanics and discrete Schr\"odinger equations).

-partially hyperbolic and non-uniformly hyperbolic dynamics;

-nonlocal and homoclinic bifurcations;

-structure of Newhouse domains (in both dissipative and conservative setting);

-applications to problems in other fields of mathematics (including celestial mechanics and discrete Schr\"odinger equations).

**Publications**

Ch. Bonatti, L. Diaz, A. Gorodetski, Non-hyperbolic ergodic measures with large support, 31 pages, arXiv:0908.4293v1.

A. Gorodetski, V. Kaloshin, Conservative homoclinic bifurcations and some applications, 27 pages, to appear in {\it Steklov Institute Proceedings}, volume 267 (dedicated to the 70th anniversary of Vladimir Arnold).

D. Damanik, A. Gorodetski, The Spectrum of the Weakly Coupled Fibonacci Hamiltonian, {\it Electronic Research Announcements in Mathematical Sciences}, vol. 16 (2009), pp. 23--29.

D. Damanik, A. Gorodetski, The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator (arXiv:0807.3024v2).

D. Damanik, A. Gorodetski, Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian, {\it Nonlinearity} {\bf 22} (2009), pp. 123--143.

L. Diaz, A. Gorodetski, Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes, {\it Ergodic Theory and Dynamical Systems}, vol. 29 (2009), pp. 1479-1513.

D. Damanik, M. Embree, A. Gorodetski, S. Tcheremchantsev, The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian, {\it Communications in Mathematical Physics}, vol. 280 (2008), no. 2, pp. 499-516.

A. Gorodetski, V. Kaloshin, How often surface diffeomorphisms exhibit infinite number of sinks, {\it Advances in Mathematics}, 208 (2007), pp.

710-797.

A. Gorodetski, B. Hunt, V. Kaloshin, Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems, vol.2, {\it Proceedings of ICM 2006, Madrid, Spain, European Math Society}, 2006, pp. 27--55.

A. Gorodetski, Regularity of central leaves of partially hyperbolic sets and applications, {\it Izvestiya RAN}, vol.70 (2006), no.6, pp. 52-78.

A. Gorodetski, Yu.S. Ilyashenko, V. Kleptsyn, M. Nalskiy, Nonremovability of zero Lyapunov exponents, {\it Functional Analysis and Applications}, vol.39 (2005), no. 1, pp. 21-30.

A. Gorodetski, Yu.S. Ilyashenko, Some properties of skew products over the horseshoe and solenoid, {\it Proceedings of the Steklov Institute of Mathematics}, vol.231 (2000), pp. 96-118.

A. Gorodetski, Yu.S. Ilyashenko, Some new robust properties of invariant sets and attractors of dynamical systems, {\it Functional Analysis and Applications}, no.2, vol.33, 1999, pp. 16-30.

A. Gorodetski, Yu.S. Ilyashenko, Minimal and strange attractors, {\it International Journal of Bifurcation and Chaos}, vol.6, no.6 (1996), pp. 1177-1183.

A. Gorodetski, Hierarchy of attractors for Axiom A diffeomorphisms, {\it Vestnik MSU}, no.1 (1996), pp. 84-86.

A. Gorodetski, V. Kaloshin, Conservative homoclinic bifurcations and some applications, 27 pages, to appear in {\it Steklov Institute Proceedings}, volume 267 (dedicated to the 70th anniversary of Vladimir Arnold).

D. Damanik, A. Gorodetski, The Spectrum of the Weakly Coupled Fibonacci Hamiltonian, {\it Electronic Research Announcements in Mathematical Sciences}, vol. 16 (2009), pp. 23--29.

D. Damanik, A. Gorodetski, The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator (arXiv:0807.3024v2).

D. Damanik, A. Gorodetski, Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian, {\it Nonlinearity} {\bf 22} (2009), pp. 123--143.

L. Diaz, A. Gorodetski, Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes, {\it Ergodic Theory and Dynamical Systems}, vol. 29 (2009), pp. 1479-1513.

D. Damanik, M. Embree, A. Gorodetski, S. Tcheremchantsev, The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian, {\it Communications in Mathematical Physics}, vol. 280 (2008), no. 2, pp. 499-516.

A. Gorodetski, V. Kaloshin, How often surface diffeomorphisms exhibit infinite number of sinks, {\it Advances in Mathematics}, 208 (2007), pp.

710-797.

A. Gorodetski, B. Hunt, V. Kaloshin, Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems, vol.2, {\it Proceedings of ICM 2006, Madrid, Spain, European Math Society}, 2006, pp. 27--55.

A. Gorodetski, Regularity of central leaves of partially hyperbolic sets and applications, {\it Izvestiya RAN}, vol.70 (2006), no.6, pp. 52-78.

A. Gorodetski, Yu.S. Ilyashenko, V. Kleptsyn, M. Nalskiy, Nonremovability of zero Lyapunov exponents, {\it Functional Analysis and Applications}, vol.39 (2005), no. 1, pp. 21-30.

A. Gorodetski, Yu.S. Ilyashenko, Some properties of skew products over the horseshoe and solenoid, {\it Proceedings of the Steklov Institute of Mathematics}, vol.231 (2000), pp. 96-118.

A. Gorodetski, Yu.S. Ilyashenko, Some new robust properties of invariant sets and attractors of dynamical systems, {\it Functional Analysis and Applications}, no.2, vol.33, 1999, pp. 16-30.

A. Gorodetski, Yu.S. Ilyashenko, Minimal and strange attractors, {\it International Journal of Bifurcation and Chaos}, vol.6, no.6 (1996), pp. 1177-1183.

A. Gorodetski, Hierarchy of attractors for Axiom A diffeomorphisms, {\it Vestnik MSU}, no.1 (1996), pp. 84-86.

**Grants**

NSF grant DMS-0901627 (2009-2012)

**Last updated**

11/17/2009