scholarly journals Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials

1983 ◽  
Vol 3 (4) ◽  
pp. 509-520 ◽  
Author(s):  
M. F. Barnsley ◽  
J. S. Geronimo ◽  
A. N. Harrington
Keyword(s):  
Orthogonal Polynomials ◽  
Complex Plane ◽  
Julia Set ◽  
Julia Sets ◽  
Moment Generating Function ◽  
Padé Approximant ◽  
Degree Polynomial ◽  
Pade Approximant ◽  
The Moment ◽  
Balanced Measure

AbstractThe Julia set B for an N'th degree polynomial T and its equilibrium electrostatic measure μ are considered. The unique balanced measure on B is shown to be μ. Integral properties of μ and of the monic polynomials orthogonal with respect to μ, Pn, n = 0, 1, 2, …, are derived. Formulae relating orthogonal polynomials of the second kind of different degrees are displayed. The measure μ is recovered both in the limit from the zeros and from the poles of the [Nn − 1/Nn] Padé approximant to the moment generating function to μ. For infinitely many polynomials of each degree N the zeros and poles all lie on an increasing sequence of trees of analytic arcs contained in B. The properties of these Padé approximant sequences support conjectures of George Baker which have not previously been tested on measures supported on sets nearly as complicated as Julia sets spread out in the complex plane.

scholarly journals Julia sets of Zorich maps

2021 ◽  
pp. 1-37
Author(s):  
ATHANASIOS TSANTARIS
Keyword(s):  
Complex Plane ◽  
Pairwise Disjoint ◽  
Exponential Family ◽  
Julia Set ◽  
Julia Sets ◽  
Three Dimensional ◽  
Periodic Points ◽  
Exponential Map ◽  
Simple Curves ◽  
Entire Complex

Abstract The Julia set of the exponential family $E_{\kappa }:z\mapsto \kappa e^z$ , $\kappa>0$ was shown to be the entire complex plane when $\kappa>1/e$ essentially by Misiurewicz. Later, Devaney and Krych showed that for $0<\kappa \leq 1/e$ the Julia set is an uncountable union of pairwise disjoint simple curves tending to infinity. Bergweiler generalized the result of Devaney and Krych for a three-dimensional analogue of the exponential map called the Zorich map. We show that the Julia set of certain Zorich maps with symmetry is the whole of $\mathbb {R}^3$ , generalizing Misiurewicz’s result. Moreover, we show that the periodic points of the Zorich map are dense in $\mathbb {R}^3$ and that its escaping set is connected, generalizing a result of Rempe. We also generalize a theorem of Ghys, Sullivan and Goldberg on the measurable dynamics of the exponential.

K+p scattering with unitary Padé approximant

1975 ◽  
Vol 87 (3) ◽  
pp. 485-508 ◽  
Author(s):  
Sarah C.B. Andrade ◽  
Erasmo Ferreira ◽  
Luis Ye Chang
Keyword(s):  
Padé Approximant ◽  
Pade Approximant

scholarly journals A generalization of the Padé approximant

1967 ◽  
Vol 20 (3) ◽  
pp. 416-420 ◽  
Author(s):  
J.L Gammel ◽  
C.C Rousseau ◽  
D.P Saylor
Keyword(s):  
Padé Approximant ◽  
Pade Approximant

Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

1971 ◽  
Vol 49 (3) ◽  
pp. 360-366
Author(s):  
D. K. Elias
Keyword(s):  
Padé Approximants ◽  
Padé Approximant ◽  
P Wave ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Wave Channel ◽  
Wave Resonance ◽  
Text Interaction ◽  
Range Of Values ◽  
D Wave

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

Heat Transfer ◽  
2022 ◽  
Author(s):  
R. S. Varun Kumar ◽  
I. E. Sarris ◽  
G. Sowmya ◽  
J. K. Madhukesh ◽  
B. C. Prasannakumara
Keyword(s):  
Electromagnetic Field ◽  
Thermal Performance ◽  
Padé Approximant ◽  
Porous Fin ◽  
Pade Approximant

Pade approximant ELF VED fields in the Earth‐Ionosphere cavity

Radio Science ◽  
2021 ◽  
Author(s):  
PengFei Liang ◽  
QingYun Di ◽  
JianBao Fan ◽  
Ruo Wang ◽  
Ya Gao
Keyword(s):  
Padé Approximant ◽  
Pade Approximant ◽  
The Earth
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