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Authors: Ruohan Yang
This article investigates the two-dimensional Brouwer Fixed-Point Theorem within the context of a surjective continuous transformation function ( f(x) ). This function can be interpreted as defining a continuous vector field. In this framework, each point in the disk is mapped to another point via a specific vector associated with the continuous transformation, thereby establishing a coherent vector field. This function can be interpreted as defining a continuous vector field. In this framework, the vector field can be decomposed two vector fields. Instead of proving the existence of fixed point directly, the article aim to focus on prove the vector fields always has intersection where at this point, the vector fields has opposite directiond and same norm.The paper also provide the programming experiment which further verifies the proof.
Comments: 12 Pages.
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[v1] 2024-10-25 17:23:04
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