Research information

I received my doctorate in 1989 from the California Institute of Technology. You can see my mathematical genealogy here.

My research interests are in dynamical systems (and differential geometry): Dynamical systems, hyperbolic (Anosov) systems; differential geometry, geodesic flows; invariant structures, rigidity. You can see reviews of my publications on MathSciNet.

Conferences in dynamical systems take place everywhere.

Publications

BOOKS


Handbook of Dynamical Systems 3 (with H.Broer & F. Takens, eds.): North Holland (in preparation)

Handbook of Dynamical Systems 1B (with A. Katok, eds.): North Holland, 2005

Modern Dynamical Systems and Applications (with M. Brin & Y. Pesin, eds.): Cambridge University Press, 2004
Dynamics: A first course (with A. Katok): Cambridge University Press, 2003
Dynamics: A first course - Paperback: Cambridge University Press, 2003
Dynamics: A first course - Russian translation: Publishing House of the Moscow Center for Continued Mathematical Education, 2005

Handbook of Dynamical Systems 1A (with A. Katok, eds.): North Holland, 2002
Introduction to the Modern Theory of Dynamical Systems (with A. Katok): Cambridge University Press, 1995 [MR 96c:58055]
Introduction to the Modern Theory of Dynamical Systems - Paperback: Cambridge University Press, 1996 [MR 96c:58055]
Introduction to the Modern Theory of Dynamical Systems - Russian Translation: Publishing House Faktorial, 1999 [MR 96c:58055]
Introduction to the Modern Theory of Dynamical Systems - Portuguese Translation: Fundação Calouste Gulbenkian, Lisboa, Portugal, 2005. [MR 96c:58055]

ARTICLES


Partially hyperbolic dynamics (with Y. Pesin): in: Handbook of Dynamical Systems, vol. 1B, North Holland, 2005
Dimension product structure of hyperbolic sets (with J. Schmeling): Electronic Research Announcements of the American Mathematical Society, 2004
Dimension product structure of hyperbolic sets (with J. Schmeling): in: Modern Dynamical Systems and Applications, pp. 331--345, Cambridge University Press, 2004
Zygmund strong foliations (with P. Foulon): Israel Journal of Mathematics 138 (2003) 157--188
Anosov and Axiom-A systems (with L.-S. Young): in: Encyclopedia of Nonlinear Science, Fitzroy Dearborn / Routledge / Taylor and Francis, 2004
Measures: in: Encyclopedia of Nonlinear Science, Fitzroy Dearborn / Routledge / Taylor and Francis, 2004
Phase space: in: Encyclopedia of Nonlinear Science, Fitzroy Dearborn / Routledge / Taylor and Francis, 2004
The Riccati equation: Pinching of forcing and solutions (with M. Gerber and D. Keesing): Experimental Mathematics 12 no. 2 (2003) 129--134
Differentiability of the Hartman--Grobman Linearization (with M. Guysinsky and V. Rayskin): Discrete and Continuous Dynamical Systems 9 no. 4 (2003) 979--984
Critical regularity of invariant foliations: Discrete and Continuous Dynamical Systems 8 no. 4 (2002) 931-937 [MR 2003g:37044]
The development of dynamics in the 20th century and the contribution of Jürgen Moser: Ergodic Theory and Dynamical Systems 22 no. 5 (2002) 1343--1364 [MR 2003h:37001]
Principal Structures (with A. Katok): in: Handbook of Dynamical Systems, vol. 1A, North Holland, 2002
Hyperbolic dynamics: in: Handbook of Dynamical Systems, vol. 1A, North Holland, 2002
Prevalence of Non-Lipschitz Anosov foliations (with A. Wilkinson): Ergodic Theory and Dynamical Systems 19 no. 3 (1999) 643-656 [MR 2000f:37035]
Prevalence of Non-Lipschitz Anosov foliations (with A. Wilkinson): Electronic Research Announcements of the American Mathematical Society 3 (1997) 93-98 [MR 98g:58140]
Regularity of the Anosov splitting III: ETH Zürich preprint 28, 1996
Regularity of the Anosov splitting II: Ergodic Theory and Dynamical Systems 17 no. 1 (1997) 169-172 [MR 98d:58135]
Regularity of the Anosov splitting and of Horospheric foliations: Ergodic Theory and Dynamical Systems 14 no. 4 (1994) 645-666 [MR 95j:58130]
Periodic bunching and invariant foliations: Mathematical Research Letters 1 no. 5 (1994) 597-600 [MR 95h:58097]
Horosperic foliations and relative pinching: Journal of Differential Geometry 39 no. 1 (1994) 57-63 [MR 95c:58137]
Anosov obstructions in higher dimension: International Journal of Mathematics 4 no. 3 (1993) 395-407 [MR 95d:58102]
Bootstrapping regularity of the Anosov splitting: Proceedings of the American Mathematical Society 115 no. 3 (1992) 817-819 [MR 92i:58138]
A Construction of the Margulis measure for Anosov flows: Ergodic Theory and Dynamical Systems 9 no. 3 (1989) 465-468 [MR 91b:58192]

You can also check with Mathematical Reviews (or read about it), for whom I am a reviewer.