American Institute of Mathematical Sciences

Advanced
July  2002, 8(3): 725-735. doi: 10.3934/dcds.2002.8.725

Tail-invariant measures for some suspension semiflows

Jon Aaronson 1, , Omri Sarig 2, and  Rita Solomyak 3,

1. 

School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
2. 

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
3. 

Department of Mathematics, University of Washington, Box 35435, Seattle, Washington 98195-4350, United States

Received  June 2001 Revised  October 2001 Published  April 2002

We consider suspension semiflows over abelian extensions of one-sided mixing subshifts of finite type. Although these are not uniquely ergodic, we identify (in the "ergodic" case) all tail-invariant, locally finite measures which are quasiinvariant for the semiflow.
Keywords: skew-products, unique ergodicity, horocycle flow., non-arithmeticity, tail-invariance, Equivalence relations, semi-flows, infinite measures, aperiodicity.
Mathematics Subject Classification: 28D05, 37A20, 37A4.
Citation: Jon Aaronson, Omri Sarig, Rita Solomyak. Tail-invariant measures for some suspension semiflows. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 725-735. doi: 10.3934/dcds.2002.8.725
[1]

François Ledrappier, Omri Sarig. Unique ergodicity for non-uniquely ergodic horocycle flows. Discrete & Continuous Dynamical Systems, 2006, 16 (2) : 411-433. doi: 10.3934/dcds.2006.16.411
[2]

Eugen Mihailescu, Mariusz Urbański. Transversal families of hyperbolic skew-products. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 907-928. doi: 10.3934/dcds.2008.21.907
[3]

Jose S. Cánovas, Antonio Falcó. The set of periods for a class of skew-products. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 893-900. doi: 10.3934/dcds.2000.6.893
[4]

Viorel Nitica. Examples of topologically transitive skew-products. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 351-360. doi: 10.3934/dcds.2000.6.351
[5]

Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012
[6]

Núria Fagella, Àngel Jorba, Marc Jorba-Cuscó, Joan Carles Tatjer. Classification of linear skew-products of the complex plane and an affine route to fractalization. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 3767-3787. doi: 10.3934/dcds.2019153
[7]

Hans Koch. On trigonometric skew-products over irrational circle-rotations. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 5455-5471. doi: 10.3934/dcds.2021084
[8]

C.P. Walkden. Stable ergodicity of skew products of one-dimensional hyperbolic flows. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 897-904. doi: 10.3934/dcds.1999.5.897
[9]

Rui Gao, Weixiao Shen. Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 2013-2036. doi: 10.3934/dcds.2014.34.2013
[10]

David Färm, Tomas Persson. Dimension and measure of baker-like skew-products of $\boldsymbol{\beta}$-transformations. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 3525-3537. doi: 10.3934/dcds.2012.32.3525
[11]

Jon Chaika, Rodrigo Treviño. Logarithmic laws and unique ergodicity. Journal of Modern Dynamics, 2017, 11: 563-588. doi: 10.3934/jmd.2017022
[12]

Charles Pugh, Michael Shub, Alexander Starkov. Unique ergodicity, stable ergodicity, and the Mautner phenomenon for diffeomorphisms. Discrete & Continuous Dynamical Systems, 2006, 14 (4) : 845-855. doi: 10.3934/dcds.2006.14.845
[13]

Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349
[14]

Henk Bruin, Gregory Clack. Inducing and unique ergodicity of double rotations. Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 4133-4147. doi: 10.3934/dcds.2012.32.4133
[15]

Dubi Kelmer. Quantum ergodicity for products of hyperbolic planes. Journal of Modern Dynamics, 2008, 2 (2) : 287-313. doi: 10.3934/jmd.2008.2.287
[16]

Roy Adler, Bruce Kitchens, Michael Shub. Errata to "Stably ergodic skew products". Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 456-456. doi: 10.3934/dcds.1999.5.456
[17]

Wenyu Pan. Joining measures for horocycle flows on abelian covers. Journal of Modern Dynamics, 2018, 12: 17-54. doi: 10.3934/jmd.2018003
[18]

Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 89-94.

[19]

Àlex Haro. On strange attractors in a class of pinched skew products. Discrete & Continuous Dynamical Systems, 2012, 32 (2) : 605-617. doi: 10.3934/dcds.2012.32.605
[20]

Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (65)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy