-
Previous Article
Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem
- JMD Home
- This Volume
-
Next Article
Invariant distributions for homogeneous flows and affine transformations
Effective decay of multiple correlations in semidirect product actions
1. | Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112-0090, United States |
References:
[1] |
M. B. Bekka, P. de la Harpe and A. Valette, Kazhdan's Property (T), Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511542749. |
[2] |
M. B. Bekka and M. Mayer, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, London Mathematical Society Lecture Note Series, 269, Cambridge University Press, Cambridge, 2000.
doi: 10.1017/CBO9780511758898. |
[3] |
M. Björklund, M. Einsiedler and A. Gorodnik, Effective multiple mixing for semisimple groups, in preparation. |
[4] |
A. Borel, Linear Algebraic Groups, Second edition, Graduate Texts in Mathematics, 126, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-0941-6. |
[5] |
M. Cowling, U. Haagerup and R. Howe, Almost $L^2$ matrix coefficients, J. Reiner Angew. Math., 387 (1988), 97-110. |
[6] |
D. Dolgopyat, Limit theorems for partially hyperbolic systems, Trans. Amer. Math. Soc., 356 (2004), 1637-1689.
doi: 10.1090/S0002-9947-03-03335-X. |
[7] |
M. Einsiedler, G. Margulis and A. Venkatesh, Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces, Invent. Math., 177 (2009), 137-212.
doi: 10.1007/s00222-009-0177-7. |
[8] |
R. E. Howe and C. C. Moore, Asymptotic properties of unitary representations, J. Funct. Anal., 32 (1979), 72-96.
doi: 10.1016/0022-1236(79)90078-8. |
[9] |
R. Howe and E. C. Tan, Non Abelian Harmonic Analysis, Universitext, Springer-Verlag, New York, 1992.
doi: 10.1007/978-1-4613-9200-2. |
[10] |
J. E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, No. 21, Springer-Verlag, New York-Heidelberg, 1975. |
[11] |
A. Katok and R. Spatzier, First cohomology of Anosov actions of higher rank Abelian groups and applications to rigidity, Inst. Hautes Études Sci. Publ. Math., 79 (1994), 131-156. |
[12] |
A. W. Knapp, Representation Theory of Semisimple Groups. An Overview Based on Examples, Princeton Landmarks in Mathematics, 36, Princeton University Press, Princeton, NJ, 1986. |
[13] |
S. Lang, Real Analysis, Second edition, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. |
[14] |
F. Ledrappier, Un champ markovien peut être d'entropie nulle et mélangeant, C. R. Acad. Sci. Paris Sér. A-B, 287 (1978), A561-A563. |
[15] |
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 17, Springer-Verlag, Berlin, 1991. |
[16] |
S. Mozes, Mixing of all orders of Lie groups actions, Inventiones Mathematicae, 107 (1992), 235-241.
doi: 10.1007/BF01231889. |
[17] |
H. Oh, Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants, Duke Mathematical Journal, 113 (2002), 133-192.
doi: 10.1215/S0012-7094-02-11314-3. |
[18] |
V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Translated from the 1991 Russian original by Rachel Rowen, Pure and Applied Mathematics, 139, Academic Press, Inc., Boston, MA, 1994. |
[19] |
K. Schmidt, Dynamical Systems of Algebraic Origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995. |
[20] |
A. N. Starkov, Dynamical Systems on Homogeneous Spaces, Translated from the 1999 Russian original by the author, Translations of Mathematical Monographs, 190, American Mathematical Society, Providence, RI, 2000. |
[21] |
M. H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1975. |
[22] |
T.-H. D. Hui, Mixing and Certain Integral Point Problems on Semisimple Lie Groups, Ph.D Thesis, Yale University, 1998. |
[23] |
Z. J. Wang, Uniform pointwise bounds for matrix coefficients of unitary representations on semidirect products, J. Funct. Anal., 267 (2014), 15-79.
doi: 10.1016/j.jfa.2014.03.014. |
[24] |
G. Warner, Harmonic Analysis on Semisimple Lie Groups I, Springer-Verlag, Berlin, 1972. |
show all references
References:
[1] |
M. B. Bekka, P. de la Harpe and A. Valette, Kazhdan's Property (T), Cambridge University Press, Cambridge, 2008.
doi: 10.1017/CBO9780511542749. |
[2] |
M. B. Bekka and M. Mayer, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, London Mathematical Society Lecture Note Series, 269, Cambridge University Press, Cambridge, 2000.
doi: 10.1017/CBO9780511758898. |
[3] |
M. Björklund, M. Einsiedler and A. Gorodnik, Effective multiple mixing for semisimple groups, in preparation. |
[4] |
A. Borel, Linear Algebraic Groups, Second edition, Graduate Texts in Mathematics, 126, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-0941-6. |
[5] |
M. Cowling, U. Haagerup and R. Howe, Almost $L^2$ matrix coefficients, J. Reiner Angew. Math., 387 (1988), 97-110. |
[6] |
D. Dolgopyat, Limit theorems for partially hyperbolic systems, Trans. Amer. Math. Soc., 356 (2004), 1637-1689.
doi: 10.1090/S0002-9947-03-03335-X. |
[7] |
M. Einsiedler, G. Margulis and A. Venkatesh, Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces, Invent. Math., 177 (2009), 137-212.
doi: 10.1007/s00222-009-0177-7. |
[8] |
R. E. Howe and C. C. Moore, Asymptotic properties of unitary representations, J. Funct. Anal., 32 (1979), 72-96.
doi: 10.1016/0022-1236(79)90078-8. |
[9] |
R. Howe and E. C. Tan, Non Abelian Harmonic Analysis, Universitext, Springer-Verlag, New York, 1992.
doi: 10.1007/978-1-4613-9200-2. |
[10] |
J. E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, No. 21, Springer-Verlag, New York-Heidelberg, 1975. |
[11] |
A. Katok and R. Spatzier, First cohomology of Anosov actions of higher rank Abelian groups and applications to rigidity, Inst. Hautes Études Sci. Publ. Math., 79 (1994), 131-156. |
[12] |
A. W. Knapp, Representation Theory of Semisimple Groups. An Overview Based on Examples, Princeton Landmarks in Mathematics, 36, Princeton University Press, Princeton, NJ, 1986. |
[13] |
S. Lang, Real Analysis, Second edition, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. |
[14] |
F. Ledrappier, Un champ markovien peut être d'entropie nulle et mélangeant, C. R. Acad. Sci. Paris Sér. A-B, 287 (1978), A561-A563. |
[15] |
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 17, Springer-Verlag, Berlin, 1991. |
[16] |
S. Mozes, Mixing of all orders of Lie groups actions, Inventiones Mathematicae, 107 (1992), 235-241.
doi: 10.1007/BF01231889. |
[17] |
H. Oh, Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants, Duke Mathematical Journal, 113 (2002), 133-192.
doi: 10.1215/S0012-7094-02-11314-3. |
[18] |
V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Translated from the 1991 Russian original by Rachel Rowen, Pure and Applied Mathematics, 139, Academic Press, Inc., Boston, MA, 1994. |
[19] |
K. Schmidt, Dynamical Systems of Algebraic Origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995. |
[20] |
A. N. Starkov, Dynamical Systems on Homogeneous Spaces, Translated from the 1999 Russian original by the author, Translations of Mathematical Monographs, 190, American Mathematical Society, Providence, RI, 2000. |
[21] |
M. H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1975. |
[22] |
T.-H. D. Hui, Mixing and Certain Integral Point Problems on Semisimple Lie Groups, Ph.D Thesis, Yale University, 1998. |
[23] |
Z. J. Wang, Uniform pointwise bounds for matrix coefficients of unitary representations on semidirect products, J. Funct. Anal., 267 (2014), 15-79.
doi: 10.1016/j.jfa.2014.03.014. |
[24] |
G. Warner, Harmonic Analysis on Semisimple Lie Groups I, Springer-Verlag, Berlin, 1972. |
[1] |
James Tanis. Exponential multiple mixing for some partially hyperbolic flows on products of $ {\rm{PSL}}(2, \mathbb{R})$. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 989-1006. doi: 10.3934/dcds.2018042 |
[2] |
Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657 |
[3] |
Ralf Spatzier, Lei Yang. Exponential mixing and smooth classification of commuting expanding maps. Journal of Modern Dynamics, 2017, 11: 263-312. doi: 10.3934/jmd.2017012 |
[4] |
Krzysztof Frączek, Leonid Polterovich. Growth and mixing. Journal of Modern Dynamics, 2008, 2 (2) : 315-338. doi: 10.3934/jmd.2008.2.315 |
[5] |
Davit Martirosyan. Exponential mixing for the white-forced damped nonlinear wave equation. Evolution Equations and Control Theory, 2014, 3 (4) : 645-670. doi: 10.3934/eect.2014.3.645 |
[6] |
Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217 |
[7] |
Xuhui Peng, Jianhua Huang, Yan Zheng. Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4479-4506. doi: 10.3934/cpaa.2020204 |
[8] |
Asaf Katz. On mixing and sparse ergodic theorems. Journal of Modern Dynamics, 2021, 17: 1-32. doi: 10.3934/jmd.2021001 |
[9] |
Lidong Wang, Xiang Wang, Fengchun Lei, Heng Liu. Mixing invariant extremal distributional chaos. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6533-6538. doi: 10.3934/dcds.2016082 |
[10] |
A. Crannell. A chaotic, non-mixing subshift. Conference Publications, 1998, 1998 (Special) : 195-202. doi: 10.3934/proc.1998.1998.195 |
[11] |
Zhi Lin, Katarína Boďová, Charles R. Doering. Models & measures of mixing & effective diffusion. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 259-274. doi: 10.3934/dcds.2010.28.259 |
[12] |
Rui Kuang, Xiangdong Ye. The return times set and mixing for measure preserving transformations. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 817-827. doi: 10.3934/dcds.2007.18.817 |
[13] |
Nir Avni. Spectral and mixing properties of actions of amenable groups. Electronic Research Announcements, 2005, 11: 57-63. |
[14] |
Richard Miles, Thomas Ward. A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1181-1189. doi: 10.3934/dcds.2011.30.1181 |
[15] |
Hadda Hmili. Non topologically weakly mixing interval exchanges. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1079-1091. doi: 10.3934/dcds.2010.27.1079 |
[16] |
Piotr Oprocha, Paweł Potorski. Topological mixing, knot points and bounds of topological entropy. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3547-3564. doi: 10.3934/dcdsb.2015.20.3547 |
[17] |
Dmitri Scheglov. Absence of mixing for smooth flows on genus two surfaces. Journal of Modern Dynamics, 2009, 3 (1) : 13-34. doi: 10.3934/jmd.2009.3.13 |
[18] |
Jean René Chazottes, F. Durand. Local rates of Poincaré recurrence for rotations and weak mixing. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 175-183. doi: 10.3934/dcds.2005.12.175 |
[19] |
Jian Li. Localization of mixing property via Furstenberg families. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 725-740. doi: 10.3934/dcds.2015.35.725 |
[20] |
Oliver Knill. Singular continuous spectrum and quantitative rates of weak mixing. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 33-42. doi: 10.3934/dcds.1998.4.33 |
2021 Impact Factor: 0.641
Tools
Metrics
Other articles
by authors
[Back to Top]