### Abstract

Let A be a Hölder continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold M. We consider the periodic data of A, i.e., the set of its return values along the periodic orbits in the base. We show that if the periodic data of A is bounded in Diffq(M), q> 1 , then the set of values of the cocycle is bounded in Diffr(M) for each r< q. Moreover, such a cocycle is isometric with respect to a Hölder continuous family of Riemannian metrics on M.

Original language | English (US) |
---|---|

Pages (from-to) | 401-417 |

Number of pages | 17 |

Journal | Geometriae Dedicata |

Volume | 202 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

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*Geometriae Dedicata*, vol. 202, no. 1, pp. 401-417. https://doi.org/10.1007/s10711-019-00421-9

**Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems.** / Sadovskaya, Victoria V.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems

AU - Sadovskaya, Victoria V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Let A be a Hölder continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold M. We consider the periodic data of A, i.e., the set of its return values along the periodic orbits in the base. We show that if the periodic data of A is bounded in Diffq(M), q> 1 , then the set of values of the cocycle is bounded in Diffr(M) for each r< q. Moreover, such a cocycle is isometric with respect to a Hölder continuous family of Riemannian metrics on M.

AB - Let A be a Hölder continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold M. We consider the periodic data of A, i.e., the set of its return values along the periodic orbits in the base. We show that if the periodic data of A is bounded in Diffq(M), q> 1 , then the set of values of the cocycle is bounded in Diffr(M) for each r< q. Moreover, such a cocycle is isometric with respect to a Hölder continuous family of Riemannian metrics on M.

UR - http://www.scopus.com/inward/record.url?scp=85060197758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060197758&partnerID=8YFLogxK

U2 - 10.1007/s10711-019-00421-9

DO - 10.1007/s10711-019-00421-9

M3 - Article

AN - SCOPUS:85060197758

VL - 202

SP - 401

EP - 417

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -