Volume 4, Issue 4
Polynomial Homogeneous Maps and Their Periods

Jaume Llibre & Violetta Pilyugina

J. Nonl. Mod. Anal., 4 (2022), pp. 753-763.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

37F10, 37C25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-753, author = {Llibre , Jaume and Pilyugina , Violetta}, title = {Polynomial Homogeneous Maps and Their Periods}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {753--763}, abstract = {

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} }
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 -

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.

Jaume Llibre & Violetta Pilyugina. (2023). Polynomial Homogeneous Maps and Their Periods. Journal of Nonlinear Modeling and Analysis. 4 (4). 753-763. doi:10.12150/jnma.2022.753
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