Limit Cycles and the Distribution of Zeros of Families of Analytic Functions
Alexander Brudnyi
Abstract
We estimate the expected number of limit cycles situated in a neighbourhood of the origin of a planar polynomial vector field. Our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter. We obtain this inequality by methods of Pluripotential Theory. This inequality also implies versions of a strong law of large numbers and the central limit theorem for a probabilistic scheme associated with the distribution of zeros.
Create a lesson
Related papers
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos et al.
On some aspects of discrete groups acting ergodically on the boundary
Subhadip Dey, Mikołaj Frączyk, Sebastian Hurtado
A Structural Theory of Admissible Transitions in Biological Reaction Networks
Stephan Peter, Bashar Ibrahim
Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
Nicola Vassena
Rigidity on the two-torus and Sarnak's conjecture
Yinshan Chang, Jian Wang, Junchang Zhou
Linear response for random systems with a cusp
Davrbek Oltiboev, Karim Rakhimov, Marks Ruziboev