HYPERBOLICITY AND SUSTAINABILITY OF ORBITS

Title & Authors
HYPERBOLICITY AND SUSTAINABILITY OF ORBITS
Fornaess, John-Erik;

Abstract
Let $\small{F: \mathbb{C}^k\;{\rightarrow}\;\mathbb{C}^k}$ be a dynamical system and let $\small{\{x_n\}_{n{\geq}0}}$ denote an orbit of F. We study the relation between $\small{\{x_n\}}$ and pseudoorbits $\small{\{y_n}, y_0=x_0.\;Here\;y_{n+1}=F(y_n)+s_n.}$ In general $\small{y_n}$ might diverge away from $\small{x_n.}$ Our main problem is whether there exists arbitrarily small $\small{t_n}$ so that if $\small{\tilde{y}_{n+1}=F(\tilde{y}_n)+s_n+t_n,}$ then $\small{\tilde{y}_n}$ remains close to $\small{x_n.}$ This leads naturally to the concept of sustainable orbits, and their existence seems to be closely related to the concept of hyperbolicity, although they are not in general equivalent.
Keywords
sustainability;complex dynamics;hyperbolicity;Henon maps;
Language
English
Cited by
References
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