SELECTED PAPERS
Translated from Russian; 19661977
 Approximation of ergodic dynamical systems by periodic transformations (with A.M.Stepin), Soviet Math. Dokl 7, (1966), 16381641
 Approximations in ergodic theory (with A.M.Stepin), Russian Math. Surveys
22 (1967), 81106

New examples in smooth ergodic theory. Ergodic diffeomorphisms (with D.V. Anosov), Trans. Moscow Math. Soc.
23 (1970), 135 (poor quality scan)

Invariant measures of flows on oriented surfaces, Soviet Math. Dokl. 14, (1973), 11041108

Topological transitivity of billiards in polygons (with A.M. Zemlyakov) Math. Notes of the Academy of Sciences of the USSR, 18, (1975), 760764;
errata 20 (1976), 1051

Theory of dynamical systems and general transformation groups with invariant measure (with Ja. G. Sinai and A.M. Stepin) Mathematical Analysis,
13 Moscow, 1975, 129261

Monotone equivalence in ergodic theory, Math. USSR Izvestija 10 (1977), 104157 (poor quality scan)

A conjecture about entropy AMS Translations 133 (1986), 91108, published in Russian in 1977
19782013
HYPERBOLICITY, ENTROPY, GEODESIC FLOWS

Bernoulli diffeomorphisms on surfaces Annals of mathematics 110 (1979), 529547

Bernoulli diffeomorphisms and group extensions of dynamical systems with nonzero characteristic exponents (with M. Brin and J. Feldman), Annals of mathematics, 113 (1981), 159179

Smooth nonBernoulli Kautomorphisms Invenetiones Math. 61 (1980), 291300

Lyapunov exponents, entropy and periodic points for diffeomorphisms Publ. Math. IHES 51 (1980), 137173

Entropy and closed geodesics Erg. Theory and Dynam. Systems 2 (Alexeyev memorial issue) (1982), 339367

Smooth models of Thurston's PseudoAnosov maps (with M. Gerber), Ann. Sci. Ecole Norm. Super. Paris 15, (1982), 173204

On local entropy (with M. Brin) Springer Lecture Notes in Math 1007 (1983), 3038

Nonuniform hyperbolicity and periodic orbits for smooth dynamical systems,Proc. Intern. Congress of Math. Warsaw 1983 2PWNNorth Holland (1984), 12451254

Random perturbations of transformations of an interval (with Yu. Kifer), J. Anal. Math., 47 (1986), 194237

Four applications of conformal equivalence to geometry and dynamics,Erg. Theory and Dynam. Systems, 8* (Conley memorial issue), (1988), 139152.

Differentiability and analyticity of topological entropy
for Anosov and geodesic flows (with G. Knieper, G. Pollicott and H. Weiss)
Invenetiones Math. 98 (1989), 581597

Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows
(with G. Knieper, and H. Weiss) Commun. Math. Phys. 138 (1991), 1931

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), 757785

Entropy and growth of expanding periodic orbits for
onedimensional maps (with A. Mezhirov), Fund. Math.,
157 (1998),
245254

Fifty years of Entropy in Dynamics: 19582007 Journal of Modern Dynamics, 1, N4, (2007), 545596.
INTERVAL EXCHANGE TRANSFORMATIONS, BILLIARDS, TWIST MAPS

Interval exchange transformations and some special flows are not mixing, Israel J. Math.
35 (1980), 301310

Some remarks on Birkhoff and Mather twist map theorems,Erg. Theory and Dynam. Systems 2, 1982), No.2, 185194

The growth rate for the number of singular and periodic orbits for a polygonal billiard
Commun. Math. Phys. 111 (1987), 151160

Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians (with D. Bernstein)
Inventiones Math. 88(1987), 225241

Weakly mixing billiards (with E. Gutkin) Springer Lecture Notes in Math
1345 (1988) 163176.

Caustics in inner and outer billiards
(with E. Gutkin),
Comm. Math. Phys., 173
(1995), 101133

Billiard table as a playground for a mathematician. (in Russian with figures); in Studencheskie
chtenja v NMU, 2 Moscow MCCME (2001), 836.
(in English without figures) ; Surveys in modern mathematics, 216242, London Math. Soc. Lecture Note Ser., 321 , Cambridge Univ. Press, Cambridge, 2005.
SPECTRAL THEORY, APPROXIMATION, COMBINATORIAL CONSTRUCTIONS

Slow entropy type invariants and smooth realization of commuting
measurepreserving transformations (with J.P. Thouvenot), Ann. Inst. H. Poincare,
33, N3 (1997),
323338

Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric
and smooth measure (with R. Gunesch), Disc. and Cont. Dyn. Sys.,
6 (2000),
6183

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),
107173;
also appears as the second part of Combinatorial constructions in ergodic theory and dynamics.

Mixed spectrum
reparameterizations of linear flows on T^{2
}(with B. Fayad and A. Windsor), Moscow
Mathematical Journal, 1, No. 4 (2001), 521537

Constructions
in elliptic dynamics (with B.Fayad), Erg. Theory and
Dynam. Systems,(Herman memorial issue), 24 (2004), 14771520 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), 649743

Some new cases of realization of spectral multiplicity function
for ergodic transformations (with M. Lemanczyk), Fundamenta Mathematicae, 206 (2009), 185215.

Analytic uniquely ergodic volume preserving maps on odd spheres(with B. Fayad), to appear in Commentarii mathematici Helvetici
CHARACTERISTIC CLASSES AND DYNAMICS

Ergodic theory and Weil measures for foliations (with S. Hurder),Annals of mathematics, 126, 1987, 221275

Differentiability, rigidity and GodbillonVey classes for Anosov flows (with S. Hurder),Publ. Math. I.H.E.S. 72, (1990), 561
COHOMOLOGY AND GEOMETRIC RIGIDITY

Anosov flows with smooth foliations and rigidity of geodesic flows on threedimensional manifolds of negative curvature (with R. Feres),
Erg. Theory and Dynam. Systems 10 (1990), 657670

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows (with R. Feres)
Erg. Theory and Dynam. Systems 9 (1989), 427432

Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori (with L. Flaminio)
Erg. Theory and Dynam. Systems 11 (1991), 427440

Local rigidity for certain groups of toral automorphisms
(with J. Lewis),
Israel J. Math, 75
(1991), 203241

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),
131156, Errata

Subelliptic estimates of polynomial differential operators and
applications to rigidity of abelian actions (with R. Spatzier), Math. Res. Letters,
1 (1994),
193202

Higher cohomology for Abelian groups of toral endomorphisms
(with S. Katok),
Erg. Theory and Dynam. Systems, 15
(1995), 569592, Errata

The cohomology of expansive
Z^{d }actions by automorphisms of compact abelian
groups
(with K. Schmidt),
Pacific. J. Math., 170
(1995), 105142

Global rigidity results
for lattice actions on tori and new examples of
volumepreserving action
(with J. Lewis),
Israel J. Math, 93
(1996), 253280

Cocycle superrigidity and rigidity for
lattice actions on tori
(with J. Lewis and R. Zimmer),
Topology, 35
(1996), 2738

Cocycle stability
for partially hyperbolic systems
(with A. Kononenko),
Math. Res. Letters, 3
(1996), 191210

Hyperbolic measures and
commuting maps in low dimension,
Disc. and Cont. Dyn. Sys, 2
(1996), 397411

Nonstationary normal forms and rigidity of
group actions (with R. Spatzier), ERAAMS, 2, N3 (1996),
124133

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),
287314

Normal forms and invariant geometric structures for dynamical systems with
invariant contracting foliations (with M. Guysinsky), Math. Res. Letters,
5 (1998),
149163

NonAbelian cohomology of abelian
Anosov actions (with V. Nitica and A.Torok), Erg.
Theory and Dynam. Systems,
20 (2000),
259288
 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), 19091917
 Periodic cycle functionals
and cocycle rigidity for certain partially hyperbolic R^{k } actions
(with D. Damjanovic), Discrete and Continuous Dynamical Systems , 13 (2005), 9851005
 Rigidity of higher rank abelian cocycles with values in diffeomorphism groups
(with V. Nitica), Geometriae Dedicata 124, No1, (2007),
109131.
 Local rigidity of restrictions of Weyl chamber flows
(with D. Damjanovic), Comptes rendus Mathematique, 344, N8 (2007), 503508.

Local rigidity of partially
hyperbolic actions. I. KAM method and Z^{k } actions on the Torus (with D. Damjanovic), Annals of Mathematics, 172 (2010), 18051858

Local rigidity of partially
hyperbolic actions.
II. The geometric method and restrictions of Weyl chamber flows on SL(n,,R)/\Gamma, (with D. Damjanovic), Int Math, Res. Notes, 2010; doi: 10.1093/imrn/rnq252.

Rigidity of realanalytic actions of SL(n,Z) on
T^{n }: A case of realization of Zimmer program (with F. Rodriguez Hertz), Discrete and Continuous Dynamical Systems , 27 (2010), 609615

Local rigidity of homogeneous parabolic actions: I. A model case (with D. Damjanovic), Journal of Modern Dynamics, 5, N2, (2011)., 203235.
MEASURE RIGIDITY

Invariant measures for higher rank hyperbolic
Abelian actions (with R. Spatzier), Erg. Theory and
Dynam. Systems, 16 (1996),
751778, Corrections to "Invariant measures for higher rank
hyperbolic Abelian actions", Erg. Theory and
Dynam. Systems, 18 (1998),
503507

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),
593637

Measurable rigidity and disjointness
for
Z^{k } actions by toral automorphisms (with B. Kalinin), Erg.
Theory and Dynam. Systems,
22 (2002),
507523

Rigidity
of measurable structure for
Z^{d } actions by automorphisms of a
torus (with S. Katok and K. Schmidt), Comm. Math. Helv., 77 (2002), 718745

Invariant measures on G/Γ for split
simple Lie
Groups G (with M. Einsiedler), Comm. Pure. Appl. Math., (Moser memorial
issue), 56 (2003), 11841221

Rigidity of measures  the high entropy case, and noncommuting foliations
(with M. Einsiedler), Israel Journal of Mathematics , 148 (2005), 169238

Invariant
measures and the set of exceptions to Littlewood's conjecture (with
M. Einsiedler and E. Lindenstrauss), Annals of Mathematics, 164 (2006), 513560
 * Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori
(with B. Kalinin), Journal of Modern Dynamics, 1, N1, (2007), 123146 ; Errata
 Uniqueness of large invariant measures for Z^{k } actions with Cartan homotopy data
(with F. Rodriguez Hertz), Journal of Modern Dynamics, 1, N2, (2007), 287300 ; Errata

New progress in nonuniform measure and cocycle rigidity (with B. Kalinin and F. Rodriguez Hertz), Electronic research Announcements in Mathematical Sciences 15, (2008), 7992.

Nonuniform measure rigidity (with B. Kalinin and F. Rodriguez Hertz),
Annals of Mathematics, 174, (2011), 361400

Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher rank abelian groups (with F. Rodriguez Hertz), Journal of Modern Dynamics, 4, N3, (2010), 487515.

Nonuniform measure rigidity for Z^{k } actions of symplectic type (with F. Rodriguez Hertz)

Arithmeticity and topology of higher rank actions of Abelian groups (with F. Rodriguez Hertz)

The Fried average entropy and slow entropy for actions of higher rank abelian groups
(with S. Katok and F. Rodriguez Hertz), to appear in Geometric and Functional Analysis.
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