A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus

Mihai Tibăr

Displaying similar documents to “A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus”

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RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the decidability of the following problem: given $p$ affine functions $f_{1}, ..., f_{p}$ over $ℕ^{k}$ and two vectors $v_{1}, v_{2} \in ℕ^{k}$ , is $v_{2}$ reachable from $v_{1}$ by successive iterations of $f_{1}, ..., f_{p}$ (in this given order)? We show that this question is decidable for $p = 1, 2$ and undecidable for some fixed $p$ .

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On homeomorphic and diffeomorphic solutions of the Abel equation on the plane

Zbigniew Leśniak (1993)

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We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.