黑洞物理是当今引力理论和天体物理学中最为活跃的研究领域，混沌是非线性动力学中一种十分重要的运动。研究黑洞时空中的混沌运动及其产生的效应是一个非常有趣且极为重要的课题。本项目致力于研究光子混沌运动对黑洞影子产生的影响。通过采用逆向光线追踪法和混沌理论中的基本方法，对光子有混沌运动时黑洞影子对黑洞参数变化的敏感性问题以及黑洞影子中的分形结构等进行系统深入的研究，找出光子混沌运动下黑洞影子对其变化敏感的参数和不敏感的参数以及它们的特征，探讨黑洞影子中自相似结构分形维度的特点及其与黑洞参数的关系。然后再研究光子运动相空间中的不变结构随黑洞参数的变化关系，找出其中对黑洞影子边界起决定性作用的因素，弄清楚黑洞影子形成过程中光子混沌运动和规则运动的作用，进而寻求光子有混沌运动时黑洞影子形成的深层次原因。本项目的研究有助于人们加深对黑洞物理和混沌动力学的理解。

Black hole physics is one of the most active research fields in gravity and astrophysics at present, and chaos is a kind of the most important motion in the nonlinear dynamics. It is a very important and interesting topic to study the chaotic motions and their corresponding effects in the black hole spacetime. In this project, we are devoted to studying effects of photon chaotic motion on the black hole shadow. Adopting the “backward ray-tracing” technique and the fundamental methods in the theory of chaos, we will investigate the sensitivity problem of shadow to the black hole parameters and the fractal structure in the shadow for various black holes under chaotic lensing. We try to find out the parameters to which black hole shadow is sensitive or insensitive and their common features under photon chaotic motion, and then make clear the relationship between the fractal dimension of the self-similar structure in the shadow and black hole parameters. Through analysing the dependence of invariant structure in phase space, including the fixed point and the invariant manifold in nonlinear dynamics, on black hole parameters, we want to find out the key factors determining the edge of black hole shadow and make clear the roles of chaotic motion and regular motion played in the formation of black hole shadow, and then try to look for the formation mechanism of black hole shadow caused by chaotic lensing. The study in this project will help us in making a deep understanding about black hole physics and chaotic dynamics.