Boundedness of hyperbolic components of Newton maps

Boundedness of hyperbolic components of Newton maps

We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we characterize the possible points on the boundary at infinity for...

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Veröffentlicht in:Israel journal of mathematics 2020-07, Vol.238 (2), p.837-869
Hauptverfasser: Nie, Hongming, Pilgrim, Kevin M.
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Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mapping
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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description We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we characterize the possible points on the boundary at infinity for some other types of hyperbolic components. For general maps, we prove hyperbolic components whose elements have fixed superattracting basins mapping by degree at least three are unbounded.
doi_str_mv 10.1007/s11856-020-2044-6
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subjects Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mapping
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
title Boundedness of hyperbolic components of Newton maps
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