A geometric approach to singularity confinement and algebraic entropy (Q2729434)
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scientific article; zbMATH DE number 1622566
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A geometric approach to singularity confinement and algebraic entropy |
scientific article; zbMATH DE number 1622566 |
Statements
A geometric approach to singularity confinement and algebraic entropy (English)
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22 July 2001
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non-autonomous cases
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rational surfaces
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intersection numbers of divisors
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algebraic entropy
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Picard group
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0.9010841
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0.88289714
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0.87950844
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0.87880063
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0.87652373
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0.87524223
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0.87363064
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The goal of this paper is to characterize one of the mappings found by \textit{J. Hietarinta} and \textit{C. Viallet} [Phys. Rev. Lett. 81, 325-328 (1998)] from the point of view of the theory of rational surfaces. As its space of initial values, the author obtains a rational surface associated with some root of indefinite type. Conversely the author recovers the mapping from the surface and consequently obtains an extension of mapping to its non-autonomous version. By considering the intersection numbers of divisors, the author presents a method to calculate the algebraic entropy of the mapping. Finally it is shown that the degree of the mapping is given by the \(n\)th power of a matrix that is given by the action of the mapping on the Picard group.
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