J. Nonl. Mod. Anal., 4 (2022), pp. 753-763.
Published online: 2023-08
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We study the set of periods of the homogeneous polynomial maps $f:\mathbb{R}^n → \mathbb{R}^n$ and $f : \mathbb{C}^n → \mathbb{C}^n$ of degree $m > 1.$ For these complex maps, we also describe the number of invariant straight lines through the origin by $f^k$ for $k = 1, 2, . . .$ and the dynamics of $f^k$ over them.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.753}, url = {http://global-sci.org/intro/article_detail/jnma/21910.html} }We study the set of periods of the homogeneous polynomial maps $f:\mathbb{R}^n → \mathbb{R}^n$ and $f : \mathbb{C}^n → \mathbb{C}^n$ of degree $m > 1.$ For these complex maps, we also describe the number of invariant straight lines through the origin by $f^k$ for $k = 1, 2, . . .$ and the dynamics of $f^k$ over them.