AI 中文总结
该研究针对保面积映射与Reeb流，证明闭三维接触流形上强非退化Reeb向量场若有至少3个简单周期轨道则存在无穷多简单正双曲周期轨道，核心结合曲面结果与破书分解定理完成证明。
AI 中文摘要
我们证明，若闭三维接触流形上的强非退化Reeb向量场至少有3个简单周期轨道，则它存在无穷多个简单正双曲周期轨道。核心依据是紧致曲面（可能带边界）上保面积映射的相关结果：在自然边界指标条件下，具有无穷多周期点的保面积非退化映射，其内部存在无穷多正双曲周期点。该证明结合了这一曲面结果与Colin-Dehornoy-Rechtman的破书分解定理。
英文摘要
We prove that a strongly nondegenerate Reeb vector field on a closed contact three-manifold has infinitely many simple positive hyperbolic periodic orbits if it has at least three simple periodic orbits. The main ingredient is a result for area-preserving maps on compact surfaces, possibly with boundary. We prove that, under a natural boundary index condition, an area-preserving nondegenerate map with infinitely many periodic points has infinitely many positive hyperbolic periodic points in the interior. The proof combines this surface result with the broken book decomposition theorem of Colin--Dehornoy--Rechtman.
Comments17 pages
