Partial Hyperbolicity in Dimension Three

Journal article

Pablo D. Carrasco, Federico Rodriguez Hertz, Jana Rodriguez Hertz, Raúl. Ures
Ergodic Theory and Dynamical Systems, vol. 8(31), 2018, pp. 2801-2837

DOI: 10.1017/etds.2016.142

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APA Click to copy
Carrasco, P. D., Rodriguez Hertz, F., Rodriguez Hertz, J., & Ures, R. (2018). Partial Hyperbolicity in Dimension Three. Ergodic Theory and Dynamical Systems, 8(31), 2801–2837. https://doi.org/10.1017/etds.2016.142

Chicago/Turabian Click to copy
Carrasco, Pablo D., Federico Rodriguez Hertz, Jana Rodriguez Hertz, and Raúl. Ures. “Partial Hyperbolicity in Dimension Three.” Ergodic Theory and Dynamical Systems 8, no. 31 (2018): 2801–2837.

MLA Click to copy
Carrasco, Pablo D., et al. “Partial Hyperbolicity in Dimension Three.” Ergodic Theory and Dynamical Systems, vol. 8, no. 31, 2018, pp. 2801–37, doi:10.1017/etds.2016.142.

BibTeX Click to copy

@article{carrasco2018a,
  title = {Partial Hyperbolicity in Dimension Three},
  year = {2018},
  issue = {31},
  journal = {Ergodic Theory and Dynamical Systems},
  pages = {2801-2837},
  volume = {8},
  doi = {10.1017/etds.2016.142},
  author = {Carrasco, Pablo D. and Rodriguez Hertz, Federico and Rodriguez Hertz, Jana and Ures, Raúl.}
}

Partial hyperbolicity appeared in the 1960s as a natural generalization of hyperbolicity. In the last 20 years, there has been great activity in this area. Here we survey the state of the art in some related topics, focusing especially on partial hyperbolicity in dimension three. The reason for this is not only that it is the smallest dimension in which non-degenerate partial hyperbolicity can occur, but also that the topology of 3-manifolds influences the dynamics in revealing ways.