Version 1
: Received: 5 September 2023 / Approved: 6 September 2023 / Online: 6 September 2023 (03:38:36 CEST)
How to cite:
Oliveira, H. Existence of Zeros for Holomorphic Complex Functions: A Dynamical Systems Approach. Preprints2023, 2023090357. https://doi.org/10.20944/preprints202309.0357.v1
Oliveira, H. Existence of Zeros for Holomorphic Complex Functions: A Dynamical Systems Approach. Preprints 2023, 2023090357. https://doi.org/10.20944/preprints202309.0357.v1
Oliveira, H. Existence of Zeros for Holomorphic Complex Functions: A Dynamical Systems Approach. Preprints2023, 2023090357. https://doi.org/10.20944/preprints202309.0357.v1
APA Style
Oliveira, H. (2023). Existence of Zeros for Holomorphic Complex Functions: A Dynamical Systems Approach. Preprints. https://doi.org/10.20944/preprints202309.0357.v1
Chicago/Turabian Style
Oliveira, H. 2023 "Existence of Zeros for Holomorphic Complex Functions: A Dynamical Systems Approach" Preprints. https://doi.org/10.20944/preprints202309.0357.v1
Abstract
This work introduces an approach to investigate the existence of zeros for holomorphic complex functions, defined on open and simply connected subdomains of C, in a systematic and direct way. This is achieved by means of the theory of dynamical systems (Poincar\'e index) and the perception that a zero of a specific complex function is an equilibtium for the associated dynamical system. The logical basis of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the function under study, assuming the existence of a zero, and investigating the consequences. Depending on the value of the index, an inconsistency may occur, establishing a contradiction.
Keywords
Holomorphic functions; Poincaré index; Zeros of complex functions
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
