TY - JOUR
T1 - Geometric expansion, Lyapunov exponents and foliations
AU - Saghin, Radu
AU - Xia, Zhihong
N1 - Funding Information:
Research supported in part by National Science Foundation. Corresponding author. E-mail addresses: rsaghin@crm.cat (R. Saghin), xia@math.northwestern.edu (Z. Xia).
PY - 2009
Y1 - 2009
N2 - We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an application, we show examples of systems with persistent non-absolute continuous center and weak unstable foliations. This generalizes the remarkable results of Shub and Wilkinson to cases where the center manifolds are not compact.
AB - We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an application, we show examples of systems with persistent non-absolute continuous center and weak unstable foliations. This generalizes the remarkable results of Shub and Wilkinson to cases where the center manifolds are not compact.
KW - Fubini's nightmare
KW - Homology of foliations
KW - Partially hyperbolic
UR - http://www.scopus.com/inward/record.url?scp=61549123693&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2008.07.001
DO - 10.1016/j.anihpc.2008.07.001
M3 - Article
AN - SCOPUS:61549123693
SN - 0294-1449
VL - 26
SP - 689
EP - 704
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 2
ER -