Compact dynamical foliations

Journal article

Pablo D. Carrasco
Ergodic Theory and Dynamical Systems, vol. 35(8), 2015, pp. 2474-2498

DOI: 10.1017/etds.2014.42

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APA Click to copy
Carrasco, P. D. (2015). Compact dynamical foliations. Ergodic Theory and Dynamical Systems, 35(8), 2474–2498. https://doi.org/10.1017/etds.2014.42

Chicago/Turabian Click to copy
Carrasco, Pablo D. “Compact Dynamical Foliations.” Ergodic Theory and Dynamical Systems 35, no. 8 (2015): 2474–2498.

MLA Click to copy
Carrasco, Pablo D. “Compact Dynamical Foliations.” Ergodic Theory and Dynamical Systems, vol. 35, no. 8, 2015, pp. 2474–98, doi:10.1017/etds.2014.42.

BibTeX Click to copy

@article{carrasco2015a,
  title = {Compact dynamical foliations},
  year = {2015},
  issue = {8},
  journal = {Ergodic Theory and Dynamical Systems},
  pages = {2474-2498},
  volume = {35},
  doi = {10.1017/etds.2014.42},
  author = {Carrasco, Pablo D.}
}

According to the work of Dennis Sullivan, there exists a smooth flow on the 5-sphere all of whose orbits are periodic although there is no uniform bound on their periods. The question addressed in this article is whether these type of examples can occur in the partially hyperbolic context. That is, if does there exist a partially hyperbolic diffeomorphism of a compact manifold such that all the leaves of its center foliation are compact but there is no uniform bound for their volumes. We develop tools to attack the previous question and show that it has negative answer provided that all periodic leaves have finite holonomy.