| Abstract: |
| In this talk we consider $C^2$ diffeomorphisms $f$ on an $n$-dimensional closed manifold $M$ $(n\ge 1)$.
We give some topological condition which guarantees that there exists at most one ($f$-invariant) hyperbolic ergodic Sinai-Ruelle-Bowen measure.
In order to give a precise statement of our result,
we denote as $P$ all periodic points $p$ whose stable and unstable sets are topological manifolds and have a topological transverse intersection at $p$.
For $m\in {\mathbb N}$ we define as $P_m$ the set of all $p\in P$ satisfying that the dimension of the stable set at $p$ is equal to $m$.
We assume that for $m\le k$, $p\in P_m$ and $q\in P_k$, the unstable set at $p$ and the stable set at $q$ have a topological transverse intersection.
Then there exists at most one hyperbolic ergodic SRB measure. |
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