October  2010, 4(4): 585-608. doi: 10.3934/jmd.2010.4.585

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

Received  January 2010 Revised  September 2010 Published  January 2011

We prove the local differentiable rigidity of generic partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from split symplectic Lie groups. We also give examples of rigidity for nongeneric actions on compact homogeneous spaces obtained from SL$(2n,\RR)$ or SL$(2n,\CC)$. The conclusions are based on the geometric approach by Katok--Damjanovic and a progress towards computations of the generating relations in these groups.
Citation: Zhenqi Jenny Wang. New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions. Journal of Modern Dynamics, 2010, 4 (4) : 585-608. doi: 10.3934/jmd.2010.4.585
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show all references

References:
[1]

(Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212.  Google Scholar

[2]

Discr. Cont. Dyn. Syst., 13 (2005), 985-1005. doi: 10.3934/dcds.2005.13.985.  Google Scholar

[3]

Int. Math. Res. Notes, 2010, to appear. Google Scholar

[4]

J. Modern Dyn., 1 (2007), 665-688.  Google Scholar

[5]

Amer. J. Math., 100 (1978), 303-386. doi: 10.2307/2373853.  Google Scholar

[6]

Springer Verlag, Berlin, 1980, 55-58.  Google Scholar

[7]

Corrected reprint of the 1978 original, Graduate Studies in Mathematics, 34, American Mathematical Society, Providence, RI, 2001.  Google Scholar

[8]

Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977.  Google Scholar

[9]

Geom. Funct. Anal., 17 (2007), 468-490. doi: 10.1007/s00039-007-0602-2.  Google Scholar

[10]

Smooth Ergodic Theory and its applications (Seattle,WA, 1999), 593-637, Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001).  Google Scholar

[11]

Math. Res. Letters, 3 (1996), 191-210.  Google Scholar

[12]

A. Katok and V. Nitica, "Differentiable Rigidity of Higher-Rank Abelian Group Actions,", Cambridge University Press, ().   Google Scholar

[13]

Inst. Hautes čtudes Sci. Publ. Math. No. 79, (1994), 131-156.  Google Scholar

[14]

Math. Res. Letters, 1 (1994), 193-202.  Google Scholar

[15]

Tr. Mat. Inst. Steklova, 216 (1997), Din. Sist. i Smezhnye Vopr., 292-319; translation in Proc. Steklov Inst. Math., 1997, 287-314.  Google Scholar

[16]

Ergebnisse derMathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 17, Springer-Verlag, Berlin, 1991.  Google Scholar

[17]

Ergodic Theory Dynam. Systems, 21 (2001), 121-164. doi: 10.1017/S0143385701001109.  Google Scholar

[18]

Ann. Sci. École Norm. Sup. (4), 2 (1969), 1–-62.  Google Scholar

[19]

Inst. Hautes Etudes Sci. Publ. Math., No. 35, (1968), 157-222.  Google Scholar

[20]

Annals of Mathematics Studies, No. 72. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971.  Google Scholar

[21]

Zürich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2004. doi: 10.4171/003.  Google Scholar

[22]

Chapman and Hall Mathematics Series. Chapman & Hall, London-New York, 1981.  Google Scholar

[23]

(French) 1962 Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) 113-127 Librairie Universitaire, Louvain; Gauthier-Villars, Paris.  Google Scholar

[24]

Yale Univ., 1967.  Google Scholar

[25]

4 (2010), 271-327. doi: 10.3934/jmd.2010.4.271.  Google Scholar

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