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| | 04-268 |
 | | It is convenient to extend each $T^n_{ij}= \kappa_j\circ T^n \circ\kappa_i^{-1}:U_{i,j,n} \to U_j$ to a $C^\infty$ diffeomorphism from $U_i$ onto its image in $\real^d_j$, still denoted by $T^n_{ij}$, in such a way that the extended map preserves the horizontal foliation and that its derivative in block form satisfies (\ref{rem0},\ref{rem}) for the same constants $\lambda_{i,j}$, $\nu_{i,j}$, $\epsilon$. |
| | \bibitem{Bow} R. Bowen, {\it Equilibrium states and the ergodic theory of Anosov diffeomorphisms,} Springer Lecture Notes in Mathematics Vol 470 (1975). |
| | For $w \in \XX$, and $\widetilde T$ an Anosov diffeomorphism on $\XX$, introduce local hyperbolicity exponents ($\cdot$ denotes euclidean norm) \begin{equation}\nonumber \begin{split} \lambda_{w}(\widetilde T)^{-1} &=\sup_{v\in E^u(\widetilde T(w)), v=1} D_{T(w)} \widetilde T^{-1} (v)\,,\cr \nu_{w}(\widetilde T)&=\sup_{v\in E^s(w), v=1} D_w\widetilde T (v)\,. |
| mpej.unige.ch /mp_arc/p/04-268 (270 words) |
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