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New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions
1. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States |
References:
[1] |
M. Brin and Y. Pesin, Partially hyperbolic dynamical systems, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212. |
[2] |
D. Damjanović and A. Katok, Periodic cycle functionals and Cocycle rigidity for certain partially hyperbolic $\RR^k$ actions, Discr. Cont. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[3] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl Chamber flows on on $\SL(n,\RR)/\Gamma$, Int. Math. Res. Notes, 2010, to appear. |
[4] |
D. Damjanovi$\acutec$, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Modern Dyn., 1 (2007), 665-688. |
[5] |
Vinay V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386.
doi: 10.2307/2373853. |
[6] |
A. J. Hahn and O. T. O'Meara, The classical groups and K-theory, Springer Verlag, Berlin, 1980, 55-58. |
[7] |
S. Helgason, "Differential Geometry, Lie Groups, and Symmetric Spaces," Corrected reprint of the 1978 original, Graduate Studies in Mathematics, 34, American Mathematical Society, Providence, RI, 2001. |
[8] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds,'' Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[9] |
B. Kalinin and R. Spatzier, On the classification of Cartan actions, Geom. Funct. Anal., 17 (2007), 468-490.
doi: 10.1007/s00039-007-0602-2. |
[10] |
B. Kalinin and A. Katok, Invariant measures for actions of higher-rank abelian groups, Smooth Ergodic Theory and its applications (Seattle,WA, 1999), 593-637, Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001). |
[11] |
A. Katok and A. Kononenko, Cocycle stability for partially hyperbolic systems, Math. Res. Letters, 3 (1996), 191-210. |
[12] |
A. Katok and V. Nitica, "Differentiable Rigidity of Higher-Rank Abelian Group Actions," Cambridge University Press, to appear. |
[13] |
A. Katok and R. Spatzier, First cohomology of Anosov actions of higher-rank abelian groups and applications to rigidity, Inst. Hautes čtudes Sci. Publ. Math. No. 79, (1994), 131-156. |
[14] |
A. Katok and R. Spatzier, Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions, Math. Res. Letters, 1 (1994), 193-202. |
[15] |
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higher-rank abelian groups and algebraic lattice actions, Tr. Mat. Inst. Steklova, 216 (1997), Din. Sist. i Smezhnye Vopr., 292-319; translation in Proc. Steklov Inst. Math., 1997, 287-314. |
[16] |
G. A.Margulis, "Discrete Subgroups Of Semisimple Lie Groups,'' Ergebnisse derMathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 17, Springer-Verlag, Berlin, 1991. |
[17] |
G. A. Margulis and N. Qian, Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices, Ergodic Theory Dynam. Systems, 21 (2001), 121-164.
doi: 10.1017/S0143385701001109. |
[18] |
H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup. (4), 2 (1969), 1–-62. |
[19] |
C. Moore, Group extensions of p-adic and adelic linear groups, Inst. Hautes Etudes Sci. Publ. Math., No. 35, (1968), 157-222. |
[20] |
J. Milnor, "Introduction to Algebraic K-theory,'' Annals of Mathematics Studies, No. 72. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. |
[21] |
Y. Pesin, "Lectures on Partial Hyperbolicity and Stable Ergodicity,'' Zürich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2004.
doi: 10.4171/003. |
[22] |
J. R. Silvester, "Introduction to Algebraic K-Theory," Chapman and Hall Mathematics Series. Chapman & Hall, London-New York, 1981. |
[23] |
R. Steinberg, Générateurs, relations et revêtements de groupes algébriques, (French) 1962 Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) 113-127 Librairie Universitaire, Louvain; Gauthier-Villars, Paris. |
[24] |
R. Steinberg, "Lecture Notes on Chevalley Groups,'' Yale Univ., 1967. |
[25] |
Zhenqi Wang, Local rigidity of partially hyperbolic actions, Journal of Modern Dynamics, 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
show all references
References:
[1] |
M. Brin and Y. Pesin, Partially hyperbolic dynamical systems, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212. |
[2] |
D. Damjanović and A. Katok, Periodic cycle functionals and Cocycle rigidity for certain partially hyperbolic $\RR^k$ actions, Discr. Cont. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[3] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl Chamber flows on on $\SL(n,\RR)/\Gamma$, Int. Math. Res. Notes, 2010, to appear. |
[4] |
D. Damjanovi$\acutec$, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Modern Dyn., 1 (2007), 665-688. |
[5] |
Vinay V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386.
doi: 10.2307/2373853. |
[6] |
A. J. Hahn and O. T. O'Meara, The classical groups and K-theory, Springer Verlag, Berlin, 1980, 55-58. |
[7] |
S. Helgason, "Differential Geometry, Lie Groups, and Symmetric Spaces," Corrected reprint of the 1978 original, Graduate Studies in Mathematics, 34, American Mathematical Society, Providence, RI, 2001. |
[8] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds,'' Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[9] |
B. Kalinin and R. Spatzier, On the classification of Cartan actions, Geom. Funct. Anal., 17 (2007), 468-490.
doi: 10.1007/s00039-007-0602-2. |
[10] |
B. Kalinin and A. Katok, Invariant measures for actions of higher-rank abelian groups, Smooth Ergodic Theory and its applications (Seattle,WA, 1999), 593-637, Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001). |
[11] |
A. Katok and A. Kononenko, Cocycle stability for partially hyperbolic systems, Math. Res. Letters, 3 (1996), 191-210. |
[12] |
A. Katok and V. Nitica, "Differentiable Rigidity of Higher-Rank Abelian Group Actions," Cambridge University Press, to appear. |
[13] |
A. Katok and R. Spatzier, First cohomology of Anosov actions of higher-rank abelian groups and applications to rigidity, Inst. Hautes čtudes Sci. Publ. Math. No. 79, (1994), 131-156. |
[14] |
A. Katok and R. Spatzier, Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions, Math. Res. Letters, 1 (1994), 193-202. |
[15] |
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higher-rank abelian groups and algebraic lattice actions, Tr. Mat. Inst. Steklova, 216 (1997), Din. Sist. i Smezhnye Vopr., 292-319; translation in Proc. Steklov Inst. Math., 1997, 287-314. |
[16] |
G. A.Margulis, "Discrete Subgroups Of Semisimple Lie Groups,'' Ergebnisse derMathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 17, Springer-Verlag, Berlin, 1991. |
[17] |
G. A. Margulis and N. Qian, Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices, Ergodic Theory Dynam. Systems, 21 (2001), 121-164.
doi: 10.1017/S0143385701001109. |
[18] |
H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup. (4), 2 (1969), 1–-62. |
[19] |
C. Moore, Group extensions of p-adic and adelic linear groups, Inst. Hautes Etudes Sci. Publ. Math., No. 35, (1968), 157-222. |
[20] |
J. Milnor, "Introduction to Algebraic K-theory,'' Annals of Mathematics Studies, No. 72. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. |
[21] |
Y. Pesin, "Lectures on Partial Hyperbolicity and Stable Ergodicity,'' Zürich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2004.
doi: 10.4171/003. |
[22] |
J. R. Silvester, "Introduction to Algebraic K-Theory," Chapman and Hall Mathematics Series. Chapman & Hall, London-New York, 1981. |
[23] |
R. Steinberg, Générateurs, relations et revêtements de groupes algébriques, (French) 1962 Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) 113-127 Librairie Universitaire, Louvain; Gauthier-Villars, Paris. |
[24] |
R. Steinberg, "Lecture Notes on Chevalley Groups,'' Yale Univ., 1967. |
[25] |
Zhenqi Wang, Local rigidity of partially hyperbolic actions, Journal of Modern Dynamics, 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
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