Abstract
We consider a direct product of a suspension flow over a substitution dynamical system and an arbitrary ergodic flow and give quantitative estimates for the speed of convergence for ergodic integrals of such systems. Our argument relies on new uniform estimates of the spectral measure for suspension flows over substitution dynamical systems. The paper answers a question by Jon Chaika.
| Original language | English |
|---|---|
| Pages (from-to) | 675-690 |
| Number of pages | 16 |
| Journal | Bulletin de la Societe Mathematique de France |
| Volume | 146 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018 Societe Mathematique de France. All rights reserved.
Funding
question that led to this work and for useful discussions. The research of A. Bufetov on this project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 647133 (ICHAOS). It was also supported by the Grant MD 5991.2016.1 of the President of the Russian Federation, by the RFBR grant 18-31-20031, by the Russian Academic Excellence Project ‘5-100’ and by the Gabriel Lamé Chair at the Chebyshev Laboratory of the SPbSU, a joint initiative of the French Embassy in the Russian Federation and Saint-Petersburg State University. B. Solomyak has been supported by the Israel Science Foundation (grant 396/15). Saint-Petersburg State University. B. Solomyak has been supported by the Israel Science Foundation (grant 396/15)
| Funders | Funder number |
|---|---|
| Israel Science Foundation | |
| SPbSU | |
| National Science Foundation | 1361424 |
| Horizon 2020 Framework Programme | MD 5991.2016.1, 647133 |
| European Commission | |
| Russian Foundation for Basic Research | 18-31-20031 |
| Israel Science Foundation | 396/15 |
| Saint Petersburg State University | |
| Ambassade de France à Moscou |
Keywords
- Hölder continuity
- Spectral measure
- Substitution dynamical system