论文标题
$ c^r $表面差异性的Lyapunov指数的最大度量和熵连续性具有较大的熵
Maximal measure and entropic continuity of Lyapunov exponents for $C^r$ surface diffeomorphisms with large entropy
论文作者
论文摘要
我们证明了Buzzi Crovisier-Sarig的Lyapunov指数的熵连续性的有限平滑版本，用于$ c^\ infty $表面差异[9]。结果，我们表明，任何$ c^r $，$ r> 1 $，带有$ h_ {top}（f）（f）> \ frac {1} {r} {r limsup_n \ frac {1} {1} {n} {n} {n} {n} \ log^+^+^+^+ \ | df^n \ $ max的措施。我们还证明了$ f $的拓扑熵的$ c^r $连续性。
We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for $C^\infty$ surface diffeomorphisms [9]. As a consequence we show that any $C^r$, $r > 1$, smooth surface diffeomorphism $f$ with $h_{top}(f) > \frac{1}{r} \limsup_n \frac{1}{n} \log^+ \|df^n\|$ admits a measure of maximal entropy. We also prove the $C^r$ continuity of the topological entropy at $f$.
