标题： 绳结和混沌在R√∂ssler系统中 显示英文标题

标题： Knots and Chaos in the R√∂ssler System

摘要： Rössler系统是众所周知的混沌动力系统之一，表现出丰富的复杂现象——然而，只有少数研究从分析角度探讨了其复杂性。 在本文中，我们找到了在某些特定参数值下Rössler系统存在混沌动力的充分条件，这些参数值下流动满足某种异宿条件。 这将使我们能够证明流动存在无限多周期轨迹，并在Rössler系统的参数空间中研究它们的分岔。 显示英文摘要

摘要： The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the existence of chaotic dynamics for the R\"ossler System at some specific parameter values at which the flow satisfies a certain heteroclinic condition. This will allow us to prove the existence of infinitely many periodic trajectories for the flow, and study their bifurcations in the parameter space of the R\"ossler system.