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Boundedness of hyperbolic components of Newton maps

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Abstract

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.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904, Israel

    Hongming Nie

  2. Department of Mathematics, Indiana University, Bloomington, Indiana, 47405, USA

    Kevin M. Pilgrim

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  1. Hongming Nie
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  2. Kevin M. Pilgrim
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Correspondence to Hongming Nie.

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Nie, H., Pilgrim, K.M. Boundedness of hyperbolic components of Newton maps. Isr. J. Math. 238, 837–869 (2020). https://doi.org/10.1007/s11856-020-2044-6

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  • DOI: https://doi.org/10.1007/s11856-020-2044-6

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