# On the ergodicity of partially hyperbolic systems

@inproceedings{Burns2005OnTE, title={On the ergodicity of partially hyperbolic systems}, author={Keith Burns and Amie Wilkinson}, year={2005} }

Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C , partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satisfied in particular by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C 1Ci partially hyperbolic systems.

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 100 CITATIONS

## Entropy along expanding foliations

VIEW 3 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Cocycles over Partially Hyperbolic Maps

VIEW 10 EXCERPTS

CITES BACKGROUND & METHODS

## Ergodicity and partial hyperbolicity on the 3-torus

VIEW 4 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## PARTIALLY HYPERBOLIC SETS WITH POSITIVE MEASURE AND ACIP FOR PARTIALLY HYPERBOLIC SYSTEMS

VIEW 4 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Denseness of ergodicity for a class of partially hyperbolic volume-preserving flows

VIEW 8 EXCERPTS

CITES RESULTS

HIGHLY INFLUENCED

## ABSOLUTE CONTINUITY, LYAPUNOV EXPONENTS AND RIGIDITY II: SYSTEMS WITH COMPACT CENTER LEAVES

VIEW 5 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Geometrical and measure-theoretic structures of maps with mostly expanding center

VIEW 3 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## Partially hyperbolic dynamics in dimension 3

VIEW 7 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Centre bunching without dynamical coherence

VIEW 4 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Problems in dynamical systems and related topics

VIEW 2 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

### FILTER CITATIONS BY YEAR

### CITATION STATISTICS

**9**Highly Influenced Citations**Averaged 11 Citations**per year from 2017 through 2019**40% Increase**in citations per year in 2019 over 2018

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 14 REFERENCES

## Better center bunching

VIEW 2 EXCERPTS

## WILKINSON, Hölder foliations

## 54

VIEW 1 EXCERPT

## SIEGMUND-SCHULTZE, Hölder continuity of the holonomy maps for hyperbolic basic sets, I, in Ergodic Theory and Related Topics, III (Güstrow

## 583

VIEW 1 EXCERPT