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Birational Maps With Sparse Post-critical Sets..pdf

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Preview of Birational maps with sparse post-critical sets.

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📊 Size: 689 KB

📄 Pages: 12 pages

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Summary

The map f extends to a birational self-map of P1 × P1 and has a sparse post-critical set. The topological entropy of f is given by htop(f) = log((1 + √5)/2), provided that the map satisfies the condition (f n) = (f)n for all n ∈ N. The condition is equivalent to the post-critical orbits of f avoiding each other. The map f preserves a meromorphic two-form η, and the support of the divisor [η] is invariant under f. The critical components of f map into the support of [η], and the post-critical sets of f are contained in the support of [η]. For negative parameters a, the map f satisfies the condition (4) in a robust fashion, and the post-critical sets of f and f^-1 are disjoint. The real dynamics of f for negative parameters a are studied, and it is shown that the post-critical sets of f and f^-1 are separated by forward and backward invariant real intervals.

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Description

The map f extends to a birational self-map of P1 × P1 and has a sparse post-critical set.

Technical Information

File Format: PDF
File Size: 689 KB
Pages: 12
Language: EN
Total Downloads: 36
Last Updated: 11 hours ago

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