论文标题
渐近造型流的渐近Maslov指数消失
Vanishing asymptotic Maslov index for conformally symplectic flows
论文作者
论文摘要
由Mather的理论最大程度地减少象征性扭曲动力学的措施，我们研究了在cotangent束上的合并符号流动。这些动力学是最有意义的动力学，可以看一下（渐近）动态MASLOV索引。我们的主要结果是在共性合成式流动的一般框架中存在消失的指数，而没有任何凸度假设。退化的扭曲条件假设意味着具有零动力学MASLOV指数的厄运不变度的存在，因此存在具有零动力学MASLOV指数的点。
Motivated by Mather theory of minimizing measures for symplectic twist dynamics, we study conformally symplectic flows on a cotangent bundle. These dynamics are the most general dynamics for which it makes sense to look at (asymptotic) dynamical Maslov index. Our main result is the existence of invariant measures with vanishing index without any convexity hypothesis, in the general framework of conformally symplectic flows. A degenerate twist-condition hypothesis implies the existence of ergodic invariant measures with zero dynamical Maslov index and thus the existence of points with zero dynamical Maslov index.
