Polynomial diffeomorphisms of ². II. Stable manifolds and recurrence
Polynomial diffeomorphisms of ². II. Stable manifolds and recurrence
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² 的多项式微分同胚。
DOI：
10.1090/s0894-0347-1991-1115786-3
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发表时间：
1991
影响因子：
3.9
通讯作者：
J. Smillie
中科院分区：
文献类型：
--
作者：
Eric Bedford;J. Smillie
F (x,y)= （y,y ax +c）这类的微分同胚具有复杂的动力学：特别是，它们具有无限多周期的周期点和正拓扑熵（参见[FM， S]）。我们可以通过考虑微分同态的迭代度的增长来区分这两类。定义deg(f)为坐标函数度数的最大值。这个量不是f的共轭不变量，因此不是动态不变量。我们可以构造一个共轭不变量，我们称之为动态度，如下：
f(x,y)= (y,y ax +c). The diffeomorphisms in this class have complicated dynamics: in particular, they have periodic points of infinitely many periods and positive topological entropy (see [FM, S]). We can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism. Define deg(f ) to be the maximum of the degrees of the coordinate functions. This quantity is not a conjugacy invariant of f, hence not a dynamical invariant. We can construct a conjugacy invariant, which we call the dynamical degree, as follows: