Non-uniformly expanding dynamics in maps with singularities and criticalities
Non-uniformly expanding dynamics in maps with singularities and criticalities
复制标题
具有奇点和临界点的地图中的非均匀扩展动态
DOI：
10.1007/bf02698857
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
W. Tucker
中科院分区：
文献类型：
--
作者：
Stefano Luzzatto;W. Tucker
在研究非经典参数值的几何Lorenz流时，我们研究了一族单参数区间映射族。我们的结论是，对于一个正的勒贝格测度集合中的所有参数，映射都有一个正的Lyapunov指数。此外，这组参数有一个密度点，它起着重要的动力作用。奇点和临界点的存在引入了有趣的动态，这一点还没有完全被理解。
We investigate a one-parameter family of interval maps arising in the study of the geometric Lorenz flow for non-classical parameter values. Our conclusion is that for all parameters in a set of positive Lebesgue measure the map has a positive Lyapunov exponent. Furthermore, this set of parameters has a density point which plays an important dynamic role. The presence of both singular and critical points introduces interesting dynamics, which have not yet been fully understood.