论文标题
总结轨道
Summable Orbits
论文作者
论文摘要
我们介绍了一类可能具有$ 0 $ lyapunov指数的轨道，但仍表现出对初始条件的敏感性。我们构建了一个可数的马尔可夫分区，几乎在任何地方都有有限的对一个，它引起的编码，并通过可总结变化来提高几何潜力（对于$ c^{1+} $ diffeemorlisl，dimension $ \ geq2 $的封闭歧管的差异性）。我们使用的一个重要工具是可能具有$ 0 $ lyapunov指数的轨道的阴影理论。 我们使用图形变换方法为这种轨道构建（弱）稳定且不稳定的叶子，并证明了这些叶子的绝对连续性W.R.T固体。特别是，我们讨论了这些叶子存在的设置，并且严格薄弱 - 即不要表现出指数缩减。一个例子是一个非均匀双曲线差异的家族，我们能够以有限的一对一方式同时对所有不变的度量进行编码。
We introduce a class of orbits which may have $0$ Lyapunov exponents, but still demonstrate some sensitivity to initial conditions. We construct a countable Markov partition with a finite-to-one almost everywhere induced coding, and which lifts the geometric potential with summable variations (for a $C^{1+}$ diffeomorphism of a closed manifold of dimension $\geq2$). An important tool we use is a shadowing theory for orbits which may have $0$ Lyapunov exponents. We construct (weak) stable and unstable leaves for such orbits using a Graph Transform method, and prove the absolute continuity of these foliations w.r.t holonomies. In particular, we discuss setups where these foliations exist, and are strictly weak -- i.e., do not demonstrate exponential contraction. One example is a family of non-uniformly hyperbolic diffeomorhpims where we are able to simultaneously code all invariant measures in a finite-to-one almost everyhwere fashion.
