论文标题
零熵的磁盘的轻度耗散差异性
Mildly dissipative diffeomorphisms of the disk with zero entropy
论文作者
论文摘要
我们通过消失的拓扑熵讨论椎间盘平滑差异性的动力学，这满足了[CP]中引入的轻度耗散特性。特别是它包含雅各布的Hénon地图，最多可达1/4。我们证明这些系统要么是（广义）Morse smale，要么是无限重新分配的。特别是，我们证明了这类差异性的构型猜想：零熵和正熵的系统集之间的界面中的任何差异性，都可以使级联反应增加一倍。这将这些表面动力学推广到Sharkovskii定理用于间隔图的众所周知的结果。
We discuss the dynamics of smooth diffeomorphisms of the disc with vanishing topological entropy which satisfy the mild dissipation property introduced in [CP]. In particular it contains the Hénon maps with Jacobian up to 1/4. We prove that these systems are either (generalized) Morse Smale or infinitely renormalizable. In particular we prove for this class of diffeomorphisms a conjecture of Tresser: any diffeomorphism in the interface between the sets of systems with zero and positive entropy admits doubling cascades. This generalizes for these surface dynamics a well known consequence of Sharkovskii's theorem for interval maps.
