Surgery on complex polynomials

On the speed of convergence of Newton’s method for complex polynomials

Mathematics of Computation ◽

10.1090/mcom/2985 ◽

2015 ◽

Vol 85 (298) ◽

pp. 693-705 ◽

Cited By ~ 2

Author(s):

Todor Bilarev ◽

Magnus Aspenberg ◽

Dierk Schleicher

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Speed Of Convergence ◽

Complex Polynomials

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Some recent results on the geometry of complex polynomials: the Gauss–Lucas theorem, polynomial lemniscates, shape analysis, and conformal equivalence

Complex Analysis and its Synergies ◽

10.1007/s40627-021-00079-8 ◽

2021 ◽

Vol 7 (2) ◽

Author(s):

Trevor J. Richards

Keyword(s):

Shape Analysis ◽

Complex Polynomials ◽

Conformal Equivalence

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Sparse complex polynomials and polynomial reducibility

Journal of Computer and System Sciences ◽

10.1016/s0022-0000(77)80013-5 ◽

1977 ◽

Vol 14 (2) ◽

pp. 210-221 ◽

Cited By ~ 23

Author(s):

David Alan Plaisted

Keyword(s):

Complex Polynomials ◽

Polynomial Reducibility

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Degree of Approximation of Real Functions by Reciprocals of Real and Complex Polynomials

SIAM Journal on Mathematical Analysis ◽

10.1137/0519017 ◽

1988 ◽

Vol 19 (1) ◽

pp. 233-245 ◽

Cited By ~ 9

Author(s):

A. L. Levin ◽

E. B. Saff

Keyword(s):

Degree Of Approximation ◽

Complex Polynomials ◽

Real Functions

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Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2014.103 ◽

2014 ◽

Vol 36 (4) ◽

pp. 1156-1166 ◽

Cited By ~ 4

Author(s):

IGORS GORBOVICKIS

Keyword(s):

Periodic Orbits ◽

Moduli Space ◽

Algebraic Independence ◽

Complex Polynomials ◽

Generic Point ◽

Algebraic Functions ◽

Polynomial Maps ◽

Affine Subspaces

We consider the space of complex polynomials of degree $n\geq 3$ with $n-1$ distinct marked periodic orbits of given periods. We prove that this space is irreducible and the multipliers of the marked periodic orbits, considered as algebraic functions on that space, are algebraically independent over $\mathbb{C}$. Equivalently, this means that at its generic point the moduli space of degree-$n$ polynomial maps can be locally parameterized by the multipliers of $n-1$ arbitrary distinct periodic orbits. We also prove a similar result for a certain class of affine subspaces of the space of complex polynomials of degree $n$.

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