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Search: MSC category 54H20 ( Topological dynamics [See also 28Dxx, 37Bxx] )

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1. 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

2. CJM 2001 (vol 53 pp. 325)

Matui, Hiroki
 Ext and OrderExt Classes of Certain Automorphisms of $C^*$-Algebras Arising from Cantor Minimal Systems Giordano, Putnam and Skau showed that the transformation group $C^*$-algebra arising from a Cantor minimal system is an $AT$-algebra, and classified it by its $K$-theory. For approximately inner automorphisms that preserve $C(X)$, we will determine their classes in the Ext and OrderExt groups, and introduce a new invariant for the closure of the topological full group. We will also prove that every automorphism in the kernel of the homomorphism into the Ext group is homotopic to an inner automorphism, which extends Kishimoto's result. Categories:46L40, 46L80, 54H20