TY - JOUR
T1 - Polynomial Homogeneous Maps and Their Periods
AU - Llibre , Jaume
AU - Pilyugina , Violetta
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 753
EP - 763
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.753
UR - https://global-sci.org/intro/article_detail/jnma/21910.html
KW - Homogeneous polynomial map, Period, Set of period, Self-map
of a sphere.
AB - <p style="text-align: justify;">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 $m &gt; 1.$ 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.</p>