论文标题
双标准地图的扩展特性
Expansion properties of Double Standard Maps
论文作者
论文摘要
对于双标准地图的家庭，$ f_ {a，b} = 2x+a+\ frac {b}π\sin2πx\ quad \ quad \ pmod {1} $，我们研究了$ a $ a $ b = 1 $的参数空间的结构，当$ b = 1 $时，当$ b \ in [0,1,1）$。在第一种情况下，地图有一个关键点，但是对于一组参数，$ e_1 $的正lebesgue度量是一个不变的绝对连续度量，用于$ f_ {a，1} $。在第二种情况下，有一个开放的非空置套装参数的$ e_b $，地图$ f_ {a，b} $正在扩展。我们表明，作为$ b \ nearrow 1 $，从测量的角度来看，$ e_b $以$ e_1 $的许多点积累。
For the family of Double Standard Maps $f_{a,b}=2x+a+\frac{b}π \sin2πx \quad\pmod{1}$ we investigate the structure of the space of parameters $a$ when $b=1$ and when $b\in[0,1)$. In the first case the maps have a critical point, but for a set of parameters $E_1$ of positive Lebesgue measure there is an invariant absolutely continuous measure for $f_{a,1}$. In the second case there is an open nonempty set $E_b$ of parameters for which the map $f_{a,b}$ is expanding. We show that as $b\nearrow 1$, the set $E_b$ accumulates on many points of $E_1$ in a regular way from the measure point of view.
