Further Strengthening of Rolle’s Theorem for Complex Polynomials

2019 ◽  
Vol 52 (3) ◽  
pp. 341-356 ◽  
Author(s):  
Blagovest Sendov ◽  
Hristo Sendov
Keyword(s):  
Complex Polynomials ◽  
Rolle’S Theorem

scholarly journals Stronger Rolle’s Theorem for Complex Polynomials

2018 ◽  
Vol 146 (8) ◽  
pp. 3367-3380 ◽  
Author(s):  
Blagovest Sendov ◽  
Hristo Sendov
Keyword(s):  
Complex Polynomials ◽  
Rolle’S Theorem

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

2015 ◽  
Vol 85 (298) ◽  
pp. 693-705 ◽  
Author(s):  
Todor Bilarev ◽  
Magnus Aspenberg ◽  
Dierk Schleicher
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Speed Of Convergence ◽  
Complex Polynomials

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

2014 ◽  
Vol 36 (4) ◽  
pp. 1156-1166 ◽  
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 $n$.

On Rolle's Theorem

1979 ◽  
Vol 86 (6) ◽  
pp. 486 ◽  
Author(s):  
Hans Samelson
Keyword(s):  
Rolle’S Theorem

How to find all roots of complex polynomials by Newton’s method

2001 ◽  
Vol 146 (1) ◽  
pp. 1-33 ◽  
Author(s):  
John Hubbard ◽  
Dierk Schleicher ◽  
Scott Sutherland
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Complex Polynomials
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