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Titlebook: Automorphisms of Affine Spaces; Arno Essen Book 1995 Springer Science+Business Media B.V. 1995 Dimension.Grad.algebraic group.algorithms.d

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On the Markus-Yamabe ConjectureThe so called . or . (MYC(n)) is as follows:.If . ∈ ..(ℝ., ℝ.) satisfies the so called Markus — Yamabe Condition, i.e. for all . ∈ ℝ. all eigenvalues of . (.) have a negative real part and if .(0) = 0, then 0 is a global attractor of the ODE
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An Algorithm that Determines whether a Polynomial Map is BijectiveOne of the central problems in the study of polynomial maps is the determination of the bijective ones. Although there are many results in the literature on this subject, they can not be used on polynomial maps of high degrees due to memory limitation or the complexity of the algorithm.
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978-90-481-4566-9Springer Science+Business Media B.V. 1995
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https://doi.org/10.1007/978-1-349-08810-2rs and ℂ:= the complex numbers. Furthermore . will denote an arbitrary field and . = (.., ..., ..): .. → .. a . i.e. a map of the form . where each .. belongs to the polynomial ring .[.]: = .[.., ..., ..].
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,Goldsmith’s Singularities and Merits,espect is “Geometric Invariant Theory” of Mumford (see [15]). The major part of the book only concerns reductive groups. More recently some work has been done to do similar things for general algebraic groups (see [8], [5], [6], [7] and [4]).
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