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Search: MSC category 34D05 ( Asymptotic properties )

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1. CJM Online first

Barros, Carlos Braga; Rocha, Victor; Souza, Josiney
Lyapunov Stability and Attraction Under Equivariant Maps
Let $M$ and $N$ be admissible Hausdorff topological spaces endowed with admissible families of open coverings. Assume that $\mathcal{S}$ is a semigroup acting on both $M$ and $N$. In this paper we study the behavior of limit sets, prolongations, prolongational limit sets, attracting sets, attractors and Lyapunov stable sets (all concepts defined for the action of the semigroup $\mathcal{S}$) under equivariant maps and semiconjugations from $M$ to $N$.

Keywords:Lyapunov stability, semigroup actions, generalized flows, equivariant maps, admissible topological spaces
Categories:37B25, 37C75, 34C27, 34D05

2. CJM 2002 (vol 54 pp. 1187)

Cobo, Milton; Gutierrez, Carlos; Llibre, Jaume
On the Injectivity of $C^1$ Maps of the Real Plane
Let $X\colon\mathbb{R}^2\to\mathbb{R}^2$ be a $C^1$ map. Denote by $\Spec(X)$ the set of (complex) eigenvalues of $\DX_p$ when $p$ varies in $\mathbb{R}^2$. If there exists $\epsilon >0$ such that $\Spec(X)\cap(-\epsilon,\epsilon)=\emptyset$, then $X$ is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Categories:34D05, 54H20, 58F10, 58F21

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