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首页> 外文期刊>Journal of the Mathematical Society of Japan >Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms
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Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms

机译：某些类型的表面亚同形具有非零扭转的轨道的存在

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The present paper concerns the dynamics of surface diffeomorphisms. Given a diffeomorphism f of a surface S, the torsion of the orbit of a point z ∈ S is, roughly speaking, the average speed of rotation of the tangent vectors under the action of the derivative of f, along the orbit of z under f. The purpose of the paper is to identify some situations where there exist measures and orbits with non-zero torsion. We prove that every area preserving diffeomorphism of the disc which coincides with the identity near the boundary has an orbit with non-zero torsion. We also prove that a diffeomorphism of the torus T~2, isotopic to the identity, whose rotation set has non-empty interior, has an orbit with non-zero torsion.
机译：本文涉及表面微晶现象的动力学。给定表面S的微分形f，大致来说，点z∈S的轨道的扭转是切线向量在f的导数作用下沿着z在f下的轨道的平均旋转速度。本文的目的是确定存在存在非零扭转量度和轨道的情况。我们证明，与边界附近的同一性一致的，保持圆盘微分的每个区域都有一个具有非零扭转的轨道。我们还证明，同位圆环T〜2的微分同构，其旋转集具有非空内部，其轨道具有非零扭转。

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