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Authors: Ruohan Yang
This article present a constructive proof by analyzing decompositions of continuous vector field. The original proof of Brouwer's theorem relies on a contradiction argument, which, while effective, does not offer a constructive method for locating the fixed point. Through projecting arbitrary vector field the basis of the vector field, it can be proved there exists zero points on both of the basis. The article will also generalize the proof from 2D to 3D dimensions. The method is also valid under surjective and scaling map.
Comments: 7 Pages.
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[v1] 2024-10-25 17:21:54
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