Ralf Spatzier

Publications


Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity
(with A. Gorodnik).

Exponential Mixing and Smooth Classification of Commuting Expanding Maps
(with L. Yang), accepted by JMD

Character Varieties and Actions on Products of Trees
(with D. Fischer, M. Larsen and M. Stover).

Equilibrium Measures for Certain Isometric Extensions of Anosov Systems
(with D. Vischer), Ergodic Theory and Dynamical Systems,

Published online: 22 September 2016, pp. 1-14. doi: 10.1017/etds.2016.62.

On the Work of Rodriguez Hertz on Rigidity in Dynamical Systems
Journal of Modern Dynamics 10 (2016), 191-207.

Positively Curved Manifolds With Large Spherical Rank
(with B. Schmidt and K. Shankar), Commentarii Mathematici Helvetici 91 (2) (2016), 219-251.

Affine Maps Between CAT(0) Spaces
(with H. Bennett and C. Mooney), Geometriae Dedicata 180 (2016), 1-16

Mixing Properties of Commuting Nilmanifold Automorphisms
(with A. Gorodnik), Acta Mathematica 215 (1) (2015), 127-159

Exponential Mixing of Nilmanifold Automorphisms
(with A. Gorodnik), Journal d'Analyse, 123 (2014), 355-396.

Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds
(with D. Fisher and B. Kalinin), JAMS v. 26 (2013), 167-198.

Totally non-symplectic Anosov actions on Tori and Nilmanifolds
(with D. Fisher and B. Kalinin), Geometry & Topology 15 (2011), 191-216.

Regularity of conjugacies of algebraic actions of Zariski dense groups
(with A. Gorodnik and T. J. Hitchman), J. Mod. Dyn. 2 (2008), no. 3, 509-540.

On the Classification of Cartan Actions
(with B. Kalinin), GAFA v. 17 (2007), p. 468-490.

Spherical rank rigidity and Blaschke manifolds
(with K. Shankar and B. Wilking), Duke J. Math. v. 128, 2005

Measurable rigidity for higher rank abelian actions
(with B. Kalinin), Ergodic Th. and Dynam. Systems, v. 25, 2005, p. 175-200

An Invitation to Rigidity Theory
in: Modern Dynamical Systems and Applications (ed. M. Brin, B. Hasselblatt, Y. Pesin), p. 211-231, Cambridge University Press 2004

Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices
(with E. Goetze), Annals of Mathematics, 150 (1999), 743--773.

Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
(with A. Katok), Dynamical systems and related topics, Proceedings of Steklov Math. Institute, v. 216, 1997, 287--314, (Editors A.A.Bolibruch, A.M. Stepin, V.V.Ryzhikov).

On Livsic's theorem, superrigidity, and Anosov actions of semisimple Lie groups
(with E. Goetze), Duke Math. J. 88 (1997), 1--27.

Non-stationary normal forms and rigidity of group actions
(with A. Katok), Elect. Res. Ann. of the AMS 2 (1996), no. 3, 124-133.

Invariant measures for higher rank hyperbolic Abelian actions
(with A. Katok), Ergod. Th. and Dynam. Syst. 16 (1996), 751--778
Corrections (PDF file).

Harmonic analysis in rigidity theory
Ergodic Theory and Its Connections With Harmonic Analysis, (Alexandria 1993), 153--205,
London Math. Soc. Lecture Note Ser. 205, Cambridge University Press, Cambridge, 1995.

First Cohomology of Anosov Actions of Higher Rank Abelian Groups And Applications to Rigidity
(with A. Katok), Publ. Math. IHES. 79 (1994), 131--156.
Errata (PDF file)

New examples of manifolds with completely integrable geodesic flows
(with G. Paternain), Advances in Math. 108, (1994), 346--366.

Subelliptic estimates of polynomial differential operators and applications to rigidity of Abelian actions
(with A. Katok), Math. Res. Letters 1 (1994), 1--11.

Riemannian manifolds with completely integrable geodesic flows
Proc. Symp. Pure Math. 54 (1993), Part 3, (ed. R. E. Greene, S.-T. Yau), 599--608.

Fundamental groups of negatively curved manifolds and actions of semisimple groups
(with R. J. Zimmer), Topology 30 (1991), 591--601.

Some examples of higher rank manifolds of nonnegative curvature
(with M. Strake), Comment. Math. Helv. 65 (1990), 299--317.

Geometrically Finite Groups, Patterson-Sullivan measures and Ratner's theorem
(with L. Flaminio), Invent. Math. 99 (1990), 601--626.

Kazhdan groups, cocycles and trees
(with S. Adams), Amer. J. of Math. 112 (1990), 271--287.

On isospectral locally symmetric spaces and a theorem of von Neumann
Duke Math. J. 59 (1989), 289--294. Correction Duke Math. J. 60 (1990), 561

Ratner's rigidity theorem for geometrically finite groups
(with L. Flaminio), in: J. C. Alexander (ed.), Dynamical Systems, Proceedings, (University of Maryland, 1986/87),
Lecture Notes in Mathematics 1342, 180--195.

Infinite Coxeter groups do not have Kazhdan's property
(with M. Bozejko and T. Januszkiewicz), J. of Operator Theory 19 (1988), 63--67.

An example of an amenable action from geometry
Ergod. Th. & Dynam. Syst. 7 (1987), 289--293.

Manifolds of nonpositive curvature and their buildings
(with K. Burns), Publ. Math. IHES 65 (1987), 35--59.

On topological Tits buildings and their classification
(with K. Burns), Publ. Math. IHES 65 (1987), 5--34.

Structure of manifolds of nonpositive curvature II
(with W. Ballmann and M. Brin), Annals of Math. 122 (1985), 204--234.

Lattices acting on boundaries of semisimple groups
Ergod. Th. and Dynam. Syst. 1 (1981), 489--494.

Dynamical Properties of Algebraic Systems
Ph.D. Thesis, University of Warwick 1983.