This article expands the framework of set-valued dynamics, focusing on transitivity, mixing, and hyper transitivity, and their applications in medicine. By generalizing these concepts to various mathematical spaces, including non-met ric and infinite-dimensional Banach spaces, and introducing multiwavelet analysis, the study provides insights into cellular behaviors in cancer dynamics. It identifies key points for therapeutic interventions and explores the impact of minor initial condition changes on tumor progression. The work bridges advanced mathematics and medicine, offering new perspectives for understanding and controlling cancer through dynamic systems and personalized approaches.

To be updated.