scholarly journals Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang-Ting Lan ◽  
Zong-Xuan Chen
Keyword(s):  
Fixed Points ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations

In this paper, we mainly study the properties of transcendental meromorphic solutionsf(z)of difference Painlevé equationsw(z+1)w(z-1)(w(z)-1)=η(z)w2(z)-λ(z)w(z)andw(z+1)w(z-1)(w(z)-1)=η(z)w(z)and obtain precise estimations of the exponents of convergence of zeros, poles ofΔf(z)andΔf(z)/f(z), and of fixed points off(z+c)for anyc∈ℂ.

scholarly journals The properties of solutions for several types of Painlevé equations concerning fixed-points, zeros and poles

2019 ◽  
Vol 17 (1) ◽  
pp. 1014-1024
Author(s):  
Hong Yan Xu ◽  
Xiu Min Zheng
Keyword(s):  
Fixed Points ◽  
Difference Equations ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Zeros And Poles

Abstract The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, Peng, Chen, and Zhang.

scholarly journals BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

2021 ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Alessandro Tanzini
Keyword(s):  
Topological String ◽  
Cluster Algebra ◽  
Painlevé Equations ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Particle Spectrum ◽  
Yang Mills ◽  
Painleve Equations ◽  
Rank One ◽  
Bilinear Equations

AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

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