Papers

PAPERS

Approximations in ergodic theory (with A.M.Stepin) Russian Math. Surveys 22 (1967), 81-106 (Scanned)
New examples in smooth ergodic theory. Ergodic diffeomorphisms,(with D.V. Anosov) Trans. Moscow Math. Soc. 23 (1970), 1-35 (Scanned)
Monotone equivalence in ergodic theory, Math. USSR Izvestija 10 (1977), 104-157 (Scanned)
Interval exchange transformations and some special flows are not mixing, Israel J. Math. 35 (1980), 301-310 (Scanned)
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity (with R. Spatzier), Publ. Math. I.H.E.S., 79 (1994), 131-156, Errata
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions (with R. Spatzier), Math. Res. Letters, 1 (1994), 193-202
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems (in collaboration with K. Burns), Erg. Theory and Dynam. Systems, 14 (1994), 757-785
Higher cohomology for Abelian groups of toral endomorphisms (with S. Katok), Erg. Theory and Dynam. Systems, 15 (1995), 569-592, Errata
The cohomology of expansive Z^d-actions by automorphisms of compact abelian groups (with K. Schmidt), Pacific. J. Math., 170 (1995), 105-142
Caustics in inner and outer billiards (with E. Gutkin), Comm. Math. Phys., 173 (1995), 101-133
Global rigidity results for lattice actions on tori and new examples of volume-preserving action (with J. Lewis), Israel J. Math, 93 (1996), 253-280
Cocycle super-rigidity and rigidity for lattice actions on tori (with J. Lewis and R. Zimmer), Topology, 35 (1996), 27-38
Invariant measures for higher rank hyperbolic Abelian actions (with R. Spatzier), Erg. Theory and Dynam. Systems, 16 (1996), 751-778, Corrections to "Invariant measures for higher rank hyperbolic Abelian actions", Erg. Theory and Dynam. Systems, 18 (1998), 503-507
Cocycle stability for partially hyperbolic systems (with A. Kononenko), Math. Res. Letters, 3 (1996), 191-210
Hyperbolic measures and commuting maps in low dimension, Disc. and Cont. Dyn. Sys, 2 (1996), 397-411
Non-stationary normal forms and rigidity of group actions (with R. Spatzier), ERA-AMS, 2, N3 (1996), 124-133
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations (with J.-P. Thouvenot), Ann. Inst. H. Poincare, 33, N3 (1997), 323-338
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions (with R. Spatzier), in Dynamical systems and related topics, (Volume dedicated to D.V. Anosov), Proc. Steklov Math. Inst , 216 (1997), 287-314
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations (with M. Guysinsky), Math. Res. Letters, 5 (1998), 149-163
Entropy and growth of expanding periodic orbits for one-dimensional maps (with A. Mezhirov), Fund. Math., 157 (1998), 245-254
Non-Abelian cohomology of abelian Anosov actions (with V. Nitica and A.Torok), Erg. Theory and Dynam. Systems, 20 (2000), 259-288
Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure (with R. Gunesch), Disc. and Cont. Dyn. Sys., 6 (2000), 61-83
Cocycles, cohomology and combinatorial constructions in ergodic theory (in collaboration with E. A. Robinson, Jr.), in Smooth Ergodic Theory and its applications, Proc. Symp. Pure Math., 69 (2001), 107-173
Invariant measures for actions of higher rank abelian groups (with B. Kalinin), in Smooth Ergodic Theory and its applications, Proc. Symp. Pure Math., 69 (2001), 593--637
Mixed Spectrum Reparameterizations of Linear Flows on T²(with B. Fayad and A. Windsor), Moscow Mathematical Journal, 1, No. 4 (2001), 521-537
Billiard table as a playground for a mathematician. (in Russian with figures); in Studencheskie chtenja v NMU, 2 Moscow MCCME (2001), 8--36. (in English without figures) ; Surveys in modern mathematics, 216--242, London Math. Soc. Lecture Note Ser., 321 , Cambridge Univ. Press, Cambridge, 2005.
Measurable rigidity and disjointness for Z^k actions by toral automorphisms (with B. Kalinin), Erg. Theory and Dynam. Systems, 22 (2002), 507-523
Rigidity of measurable structure for Z^d actions by automorphisms of a torus (with S. Katok and K. Schmidt), Comm. Math. Helv., 77 (2002), 718-745
The development of dynamics in the 20th century and contribution of Jurgen Moser (with B. Hasselblatt), Erg. Theory and Dynam. Systems, (Moser memorial issue) 22 (2002), 1343-1364
Invariant measures on G/Γ for split simple Lie Groups G (with M. Einsiedler), Comm. Pure. Appl. Math., (Moser memorial issue), 56 (2003), 1184-1221
Constructions in elliptic dynamics (with B.Fayad), Erg. Theory and Dynam. Systems,(Herman memorial issue), 24 (2004), 1477-1520 with an error in the published version corrected
Spectral properties and combinatorial constructions in ergodic theory (with J.-P.Thouvenot), Handbook in Dynamical systems, vol. 1B, Elsevier, (2005), 649-743
Rigidity of measures -- the high entropy case, and non-commuting foliations (with M. Einsiedler), Israel Journal of Mathematics , 148 (2005), 169-238
Higher cohomology for Abelian groups of toral automorphisms II: the partially hyperbolic case, and corrigendum (with S. Katok), Erg. Theory and Dynam. Systems, 25 (2005), 1909-1917
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic R^k actions (with D. Damjanovic), Discrete and Continuous Dynamical Systems , 13 (2005), 985-1005
Invariant measures and the set of exceptions to Littlewood's conjecture (with M. Einsiedler and E. Lindenstrauss), Annals of Mathematics, 164 (2006), 513--560
Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori (with B. Kalinin), Journal of Modern Dynamics, 1, N1, (2007), 123--146
Uniqueness of large invariant measures for Z^k actions with Cartan homotopy data (with F. Rodriguez Hertz), Journal of Modern Dynamics, 1, N2, (2007), 287--300
Rigidity of higher rank abelian cocycles with values in diffeomorphism groups (with V. Nitica), Geometriae Dedicata 124, No1, (2007), 109-131.

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Last updated on April 22, 2009