American Institute of Mathematical Sciences

Advanced
January  2010, 26(1): 365-378. doi: 10.3934/dcds.2010.26.365

Absolutely continuous spectrum of some group extensions of Gaussian actions

Dariusz Skrenty 1,

1. 

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Received  February 2009 Revised  July 2009 Published  October 2009

Group extensions of Gaussian $\mathbb{G}$-actions with absolutely continuous spectrum in the orthocomplement of the functions depending on the first coordinate are constructed for $\mathbb{G}$ equal to $\mathbb{Z}^{d}$, $d\in\mathbb{N}\cup\{\infty\}$ or $\mathbb{Q}$.
Keywords: absolutely continuous spectrum., Gaussian actions, cocycles.
Mathematics Subject Classification: Primary: 37A15, 37A20; Secondary: 60G1.
Citation: Dariusz Skrenty. Absolutely continuous spectrum of some group extensions of Gaussian actions. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 365-378. doi: 10.3934/dcds.2010.26.365
[1]

Lucia D. Simonelli. Absolutely continuous spectrum for parabolic flows/maps. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 263-292. doi: 10.3934/dcds.2018013
[2]

Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete & Continuous Dynamical Systems, 2019, 39 (9) : 5105-5124. doi: 10.3934/dcds.2019207
[3]

Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete & Continuous Dynamical Systems, 2019, 39 (5) : 2393-2412. doi: 10.3934/dcds.2019101
[4]

Fanni M. Sélley. A self-consistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 9-32. doi: 10.3934/jcd.2021002
[5]

H. Bercovici, V. Niţică. Cohomology of higher rank abelian Anosov actions for Banach algebra valued cocycles. Conference Publications, 2001, 2001 (Special) : 50-55. doi: 10.3934/proc.2001.2001.50
[6]

Oliver Knill. Singular continuous spectrum and quantitative rates of weak mixing. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 33-42. doi: 10.3934/dcds.1998.4.33
[7]

Jawad Al-Khal, Henk Bruin, Michael Jakobson. New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 35-61. doi: 10.3934/dcds.2008.22.35
[8]

Jiu Ding, Aihui Zhou. Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 451-458. doi: 10.3934/dcds.2000.6.451
[9]

Brittany Froese Hamfeldt. Convergent approximation of non-continuous surfaces of prescribed Gaussian curvature. Communications on Pure & Applied Analysis, 2018, 17 (2) : 671-707. doi: 10.3934/cpaa.2018036
[10]

Felipe A. Ramírez. Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups. Journal of Modern Dynamics, 2009, 3 (3) : 335-357. doi: 10.3934/jmd.2009.3.335
[11]

Bassam Fayad, A. Windsor. A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Journal of Modern Dynamics, 2007, 1 (1) : 107-122. doi: 10.3934/jmd.2007.1.107
[12]

Jordi-Lluís Figueras, Thomas Ohlson Timoudas. Sharp $ \frac12 $-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4519-4531. doi: 10.3934/dcds.2020189
[13]

Darren C. Ong. Orthogonal polynomials on the unit circle with quasiperiodic Verblunsky coefficients have generic purely singular continuous spectrum. Conference Publications, 2013, 2013 (special) : 605-609. doi: 10.3934/proc.2013.2013.605
[14]

Eduardo Garibaldi, Irene Inoquio-Renteria. Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property. Discrete & Continuous Dynamical Systems, 2020, 40 (4) : 2315-2333. doi: 10.3934/dcds.2020115
[15]

C. T. Cremins, G. Infante. A semilinear $A$-spectrum. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 235-242. doi: 10.3934/dcdss.2008.1.235
[16]

A. Kononenko. Twisted cocycles and rigidity problems. Electronic Research Announcements, 1995, 1: 26-34.

[17]

Franz W. Kamber and Peter W. Michor. Completing Lie algebra actions to Lie group actions. Electronic Research Announcements, 2004, 10: 1-10.

[18]

Leonid Berlyand, Giuseppe Cardone, Yuliya Gorb, Gregory Panasenko. Asymptotic analysis of an array of closely spaced absolutely conductive inclusions. Networks & Heterogeneous Media, 2006, 1 (3) : 353-377. doi: 10.3934/nhm.2006.1.353
[19]

Luis Barreira, Claudia Valls. Noninvertible cocycles: Robustness of exponential dichotomies. Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 4111-4131. doi: 10.3934/dcds.2012.32.4111
[20]

Dmitry Dolgopyat, Dmitry Jakobson. On small gaps in the length spectrum. Journal of Modern Dynamics, 2016, 10: 339-352. doi: 10.3934/jmd.2016.10.339

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences