Dynamical behavior of endomorphisms on certain invariant sets

Rok, strany: 2013, 135 - 142

We study the Hausdorff dimension of the intersection between local stable manifolds and the respective basic sets of a class of hyperbolic polynomial endomorphisms on the complex projective space $\mathbb{P}²$. We consider the perturbation $(z²+ε z+bε w²,w²)$ of $(z²,w²)$ and we prove that, for $b$ sufficiently small, it is injective on its basic set $Λ_ε$ close to $Λ:=\{0\}× S¹$. Moreover we give very precise upper and lower estimates for the Hausdorff dimension of the intersection between local stable manifolds and $Λ_ε$, in the case of these maps.

ISO 690:

Putan, D., Stan, D. 2013. Dynamical behavior of endomorphisms on certain invariant sets. In Mathematica Slovaca, vol. 63, no.1, pp. 135-142. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0088-8

APA:

Putan, D., Stan, D. (2013). Dynamical behavior of endomorphisms on certain invariant sets. Mathematica Slovaca, 63(1), 135-142. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0088-8