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A Review of Chaotic Dynamics in Set-Valued Maps and Its Applications in Modeling Cellular Proliferation and Cancer Evolution

Abstract:

This article reviews the framework of set-valued dynamics, focusing on transitivity, mixing, and hypercyclicity, and their applications in medicine. By generalizing these concepts to various mathematical spaces, the study provides insight 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.