Abstract
Let \(F: {\mathbb {R}}^2\rightarrow {\mathbb {R}}^2\) be a polynomial mapping. We consider the image of the compositions \(F^k\) of F. We prove that under some condition then the image of the iterated map \(F^k\) is stable when k is large.
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Acknowledgements
The author would like to thank Professor Ha Huy Vui for introducing him to this problem. We also thank the anonymous referee(s) for his/her corrections and valuable comments.
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Dedicate to the 60th birthday of Professor Osamu Saeki.
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This work was supported by the Vietnam Academy of Science and Technology under Grant Number ƉLTE00.04/23-24.
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Nguyen, T.T. Image of iterated polynomial maps of the real plane. Res Math Sci 11, 16 (2024). https://doi.org/10.1007/s40687-024-00433-2
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DOI: https://doi.org/10.1007/s40687-024-00433-2