
Previous Article
Measures invariant under horospherical subgroups in positive characteristic
 JMD Home
 This Issue
 Next Article
Local rigidity of homogeneous parabolic actions: I. A model case
1.  Department of Mathematics, Rice University, 6100 Main St., Houston, TX 77005, United States 
2.  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
References:
[1] 
E. J. Benveniste, Rigidity of isometric lattice actions on compact Riemannian manifolds, Geom. Funct. Anal., 10 (2000), 516542. doi: 10.1007/PL00001627. 
[2] 
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665688. doi: 10.3934/jmd.2007.1.665. 
[3] 
D. Damjanović and A. Katok, Local rigidity of restrictions of Weyl chamber flows, C. R. Math. Acad. Sci. Paris, 344 (2007), 503508. 
[4] 
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n, R)$$/\Gamma$, Int. Math. Res. Notes, 2010. doi: 10.1093/imrn/rnq252. 
[5] 
D. Damjanović and A. Katok, Local rigidity of actions of higherrank abelian groups and KAM method, Electron. Res. Announc. Amer. Math. Soc., 10 (2004), 142154. 
[6] 
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\Z^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 18051858. 
[7] 
D. Fisher, First cohomology and local rigidity of group actions,, Ann. of Math., (). 
[8] 
L. Flaminio and G. Forni, Invariant distributions and time averages for horocycle flows, Duke Math. J., 119 (2003), 465526. 
[9] 
R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 65222. 
[10] 
B. Hasselblatt and A. Katok, Principal structures, in "Handbook in Dynamical Systems," 1A, NorthHolland, Amsterdam, (2002), 1203. 
[11] 
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higherrank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math., 216 (1997), 287314. 
[12] 
D. Mieczkowski, The first cohomology of parabolic actions for some higherrank abelian groups and representation theory, J. Mod. Dyn., 1 (2007), 6192. doi: 10.3934/jmd.2007.1.61. 
[13] 
D. Mieczkowski, "The Cohomological Equation and Representation Theory," Ph.D thesis, The Pennsylvania State University, 2006. 
[14] 
J. Moser, On commuting circle mappings and simoultaneous Diophantine approximations, Math. Z., 205 (1990), 105121. doi: 10.1007/BF02571227. 
[15] 
F. Ramirez, Cocycles over higherrank abelian actions on quotients of semisimple Lie groups, J. Mod. Dyn., 3 (2009), 335357. doi: 10.3934/jmd.2009.3.335. 
[16] 
E. Zehnder, Generalized implicitfunction theorems with applications to some small divisor problems. I, Comm. Pure Appl. Math., 28 (1975), 91140. 
[17] 
Z. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271327. doi: 10.3934/jmd.2010.4.271. 
[18] 
Z. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585608. doi: 10.3934/jmd.2010.4.585. 
show all references
References:
[1] 
E. J. Benveniste, Rigidity of isometric lattice actions on compact Riemannian manifolds, Geom. Funct. Anal., 10 (2000), 516542. doi: 10.1007/PL00001627. 
[2] 
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665688. doi: 10.3934/jmd.2007.1.665. 
[3] 
D. Damjanović and A. Katok, Local rigidity of restrictions of Weyl chamber flows, C. R. Math. Acad. Sci. Paris, 344 (2007), 503508. 
[4] 
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n, R)$$/\Gamma$, Int. Math. Res. Notes, 2010. doi: 10.1093/imrn/rnq252. 
[5] 
D. Damjanović and A. Katok, Local rigidity of actions of higherrank abelian groups and KAM method, Electron. Res. Announc. Amer. Math. Soc., 10 (2004), 142154. 
[6] 
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\Z^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 18051858. 
[7] 
D. Fisher, First cohomology and local rigidity of group actions,, Ann. of Math., (). 
[8] 
L. Flaminio and G. Forni, Invariant distributions and time averages for horocycle flows, Duke Math. J., 119 (2003), 465526. 
[9] 
R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 65222. 
[10] 
B. Hasselblatt and A. Katok, Principal structures, in "Handbook in Dynamical Systems," 1A, NorthHolland, Amsterdam, (2002), 1203. 
[11] 
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higherrank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math., 216 (1997), 287314. 
[12] 
D. Mieczkowski, The first cohomology of parabolic actions for some higherrank abelian groups and representation theory, J. Mod. Dyn., 1 (2007), 6192. doi: 10.3934/jmd.2007.1.61. 
[13] 
D. Mieczkowski, "The Cohomological Equation and Representation Theory," Ph.D thesis, The Pennsylvania State University, 2006. 
[14] 
J. Moser, On commuting circle mappings and simoultaneous Diophantine approximations, Math. Z., 205 (1990), 105121. doi: 10.1007/BF02571227. 
[15] 
F. Ramirez, Cocycles over higherrank abelian actions on quotients of semisimple Lie groups, J. Mod. Dyn., 3 (2009), 335357. doi: 10.3934/jmd.2009.3.335. 
[16] 
E. Zehnder, Generalized implicitfunction theorems with applications to some small divisor problems. I, Comm. Pure Appl. Math., 28 (1975), 91140. 
[17] 
Z. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271327. doi: 10.3934/jmd.2010.4.271. 
[18] 
Z. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585608. doi: 10.3934/jmd.2010.4.585. 
[1] 
Danijela Damjanovic and Anatole Katok. Local rigidity of actions of higher rank abelian groups and KAM method. Electronic Research Announcements, 2004, 10: 142154. 
[2] 
Masayuki Asaoka. Local rigidity of homogeneous actions of parabolic subgroups of rankone Lie groups. Journal of Modern Dynamics, 2015, 9: 191201. doi: 10.3934/jmd.2015.9.191 
[3] 
Zhenqi Jenny Wang. Local rigidity of partially hyperbolic actions. Journal of Modern Dynamics, 2010, 4 (2) : 271327. doi: 10.3934/jmd.2010.4.271 
[4] 
Zhenqi Jenny Wang. Local rigidity of partially hyperbolic actions. Electronic Research Announcements, 2010, 17: 6879. doi: 10.3934/era.2010.17.68 
[5] 
Qiao Liu. Local rigidity of certain solvable group actions on tori. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 553567. doi: 10.3934/dcds.2020269 
[6] 
Woochul Jung, Keonhee Lee, Carlos Morales, Jumi Oh. Rigidity of random group actions. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 68456854. doi: 10.3934/dcds.2020130 
[7] 
Mao Okada. Local rigidity of certain actions of solvable groups on the boundaries of rankone symmetric spaces. Journal of Modern Dynamics, 2021, 17: 111143. doi: 10.3934/jmd.2021004 
[8] 
A. Katok and R. J. Spatzier. Nonstationary normal forms and rigidity of group actions. Electronic Research Announcements, 1996, 2: 124133. 
[9] 
Danijela Damjanović, James Tanis. Cocycle rigidity and splitting for some discrete parabolic actions. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 52115227. doi: 10.3934/dcds.2014.34.5211 
[10] 
James Tanis, Zhenqi Jenny Wang. Cohomological equation and cocycle rigidity of discrete parabolic actions. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 39694000. doi: 10.3934/dcds.2019160 
[11] 
Manfred Einsiedler and Elon Lindenstrauss. Rigidity properties of \zdactions on tori and solenoids. Electronic Research Announcements, 2003, 9: 99110. 
[12] 
Andrei Török. Rigidity of partially hyperbolic actions of property (T) groups. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 193208. doi: 10.3934/dcds.2003.9.193 
[13] 
Federico Rodriguez Hertz. Global rigidity of certain Abelian actions by toral automorphisms. Journal of Modern Dynamics, 2007, 1 (3) : 425442. doi: 10.3934/jmd.2007.1.425 
[14] 
Danijela Damjanovic, James Tanis, Zhenqi Jenny Wang. On globally hypoelliptic abelian actions and their existence on homogeneous spaces. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 67476766. doi: 10.3934/dcds.2020164 
[15] 
Kaifang Liu, Lunji Song, Shan Zhao. A new overpenalized weak galerkin method. Part Ⅰ: Secondorder elliptic problems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 24112428. doi: 10.3934/dcdsb.2020184 
[16] 
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new overpenalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25812598. doi: 10.3934/dcdsb.2020196 
[17] 
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123146. doi: 10.3934/jmd.2007.1.123 
[18] 
Jonathan DeWitt. Local Lyapunov spectrum rigidity of nilmanifold automorphisms. Journal of Modern Dynamics, 2021, 17: 65109. doi: 10.3934/jmd.2021003 
[19] 
Boris Kalinin, Anatole Katok, Federico Rodriguez Hertz. Errata to "Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori" and "Uniqueness of large invariant measures for $\Zk$ actions with Cartan homotopy data". Journal of Modern Dynamics, 2010, 4 (1) : 207209. doi: 10.3934/jmd.2010.4.207 
[20] 
Xuanji Hou, Lei Jiao. On local rigidity of reducibility of analytic quasiperiodic cocycles on $U(n)$. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 31253152. doi: 10.3934/dcds.2016.36.3125 
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]