scholarly journals Hyperbolic polynomial diffeomorphisms of C2. I: A non-planar map

2008 ◽  
Vol 218 (2) ◽  
pp. 417-464 ◽  
Author(s):  
Yutaka Ishii
Keyword(s):  
Hyperbolic Polynomial ◽  
Planar Map ◽  
Polynomial Diffeomorphisms

scholarly journals Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mina Ketan Mahanti ◽  
Amandeep Singh ◽  
Lokanath Sahoo
Keyword(s):  
Random Variables ◽  
Random Coefficients ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Gaussian Random Variables ◽  
Hyperbolic Polynomials ◽  
Asymptotic Value ◽  
Real Zeros ◽  
Number Of Real Zeros

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the formy=Pnt=n1a1cosh⁡t+n2a2cosh⁡2t+⋯+nnancosh⁡nt, wherea1,…,anis a sequence of standard Gaussian random variables, isn/2+op(1). It is shown that the asymptotic value of expected number of times the polynomial crosses the levely=Kis alson/2as long asKdoes not exceed2neμ(n), whereμ(n)=o(n). The number of oscillations ofPn(t)abouty=Kwill be less thann/2asymptotically only ifK=2neμ(n), whereμ(n)=O(n)orn-1μ(n)→∞. In the former case the number of oscillations continues to be a fraction ofnand decreases with the increase in value ofμ(n). In the latter case, the number of oscillations reduces toop(n)and almost no trace of the curve is expected to be present above the levely=Kifμ(n)/(nlogn)→∞.

Random Boundary of a Planar Map

2002 ◽  
pp. 83-93 ◽  
Author(s):  
Maxim Krikun ◽  
Vadim Malyshev
Keyword(s):  
Random Boundary ◽  
Planar Map

scholarly journals Analytic invariant curves for a planar map

2002 ◽  
Vol 15 (5) ◽  
pp. 567-573 ◽  
Author(s):  
Jian-Guo Si ◽  
Xin-Ping Wang ◽  
Wei-Nian Zhang
Keyword(s):  
Invariant Curves ◽  
Planar Map ◽  
Analytic Invariant

Planar Map Generation by Parallel Binary Fission/Fusion Grammars

The Book of L ◽  
1986 ◽  
pp. 29-43 ◽  
Author(s):  
Jack W. Carlyle ◽  
Sheila A. Greibach ◽  
Azaria Paz
Keyword(s):  
Binary Fission ◽  
Planar Map ◽  
Map Generation

scholarly journals Every planar map is four colorable. Part II: Reducibility

1977 ◽  
Vol 21 (3) ◽  
pp. 491-567 ◽  
Author(s):  
K. Appel ◽  
W. Haken ◽  
J. Koch
Keyword(s):  
Planar Map
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