Geodesic
Dynamics of a family of maps defined by quadratic polynomials
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 4, pp. 447-465.

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We consider maps $F \colon {\mathbb R}^{2} \rightarrow \mathbb R^{2}$, whose coordinates are homogeneous polynomials in $\mathbb R[x, y]$ of degree $2$. These maps send lines passing through the origin into lines passing through the origin. Our goal is to study how these lines are moved under the action of $F$. We show that there is a real analytic variety $\mathcal{F}^{2}$, where two sets can be clearly distinguished. One set $\mathcal{U} \subseteq \mathcal{F}^{2}$ is made up of transformations that have "hidden hyperbolic" dynamics, and its complement $\mathcal{F}^{2} \setminus \mathcal{U}$ contains maps that show a chaotic behavior.
Keywords: polynomial map, circle map, chaotic dynamics. 
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J. Jaurez-Rosas; H. Méndez. Dynamics of a family of maps defined by quadratic polynomials. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 4, pp. 447-465. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_4_a4/

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