Abstract: Tracking Any Point (TAP) plays a crucial role in motion analysis. Video-based approaches rely on iterative local matching for tracking, but they assume linear motion during the blind time between frames, which leads to point loss under large displacements or nonlinear motion. The high temporal resolution and motion blur-free characteristics of event cameras provide continuous, fine-grained motion information, capturing subtle variations with microsecond precision. This paper presents an event-based framework for tracking any point, which tackles the challenges posed by spatial sparsity and motion sensitivity in events through two tailored modules. Specifically, to resolve ambiguities caused by event sparsity, a motion-guidance module incorporates kinematic vectors into the local matching process. Additionally, a variable motion aware module is integrated to ensure temporally consistent responses that are insensitive to varying velocities, thereby enhancing matching precision.To validate the effectiveness of the approach, two event dataset for tracking any point is constructed by simulation. The method improves the $Survival_{50}$ metric by 17.9\% over event-only tracking of any point baseline. Moreover, on standard feature tracking benchmarks, it outperforms all existing methods, even those that combine events and video frames.