Rigidity for real polynomials

Hyperbolicity is Dense in the Real Quadratic Family

It is shown that for non-hyperbolic real quadratic polynomials topological and qua-sisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps are dense. Statement of the results. Dense Hyperbolicity Theorem In the real quadratic family f a (x) = ax(1 − x) , 0 < a ≤ 4 the mapping f a ha...

On Classifications of Random Polynomials

&nbsp;Let $ a_0&nbsp;(omega),&nbsp;a_1&nbsp;(omega),&nbsp;a_2&nbsp;(omega), dots,&nbsp;a_n&nbsp;(omega)$&nbsp;be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr,&nbsp;A)$. There are many known results for the expected number of real zeros of a polynomial&nbsp;$ a_0&nbsp;(omega) psi_0(x)+&nbsp;a_1&nbsp;(omega)psi_1 (x)+,&nbsp;a_2&nbsp;(omega)psi_2 (x)+...

On the Borderline of Real and Complex Dynamics

1.1. Overview. We will describe recent developments in several intimately related problems of complex and real one-dimensional dynamics: rigidity of polynomials and local connectivity of the Mandelbrot set, measure of Julia sets, and attractors of quasi-quadratic maps. A combinatorial basis for this study is provided by the Yoccoz puzzle. The main problem is to understand the geometry of the pu...

استخراج چسبندگی قیمتی در اقتصاد ایران در قالب مدل تعادل عمومی پویای تصادفی

&nbsp; Structural parameters are necessary and important in some economic studies, especially in general equilibrium models. One of these structural parameters is degree of price rigidity. In this article we try estimate degree of price rigidity in Iran economy in a General Equilibrium Dynamic Stochastic Model with Bayesian method. Our result with using seasonal data of real consumption, GDP...

On the average number of sharp crossings of certain Gaussian random polynomials