46 citations · 60 across the 9 of their papers we have counts for
7 papers · 1 filter
Hyperbolic-parabolic deformations of rational maps
Guizhen Cui, Lei Tan
We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in ce…
Kneading with weights
Hans Henrik Rugh, Lei Tan
We generalise Milnor-Thurston's kneading theory to the setting of piecewise continuous and monotone interval maps with weights. We define a weighted kneading determinant ${\cal D}(…
On Parameter Space of Complex Polynomial Vector Fields in the Complex Plane
Kealey Dias, Lei Tan
The space of degree d single-variable monic and centered complex polynomial vector fields can be decomposed into loci in which the vector fields have the same topological structure…
Renormalizations and wandering Jordan curves of rational maps
Guizhen Cui, Wenjuan Peng, Lei Tan
We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant…
Combinatorial rigidity of multicritical maps
Wenjuan Peng, Lei Tan
We combine the KSS nest constructed by Kozlovski, Shen and van Strien, and the analytic method proposed by Avila, Kahn, Lyubich and Shen to prove the combinatorial rigidity of mult…
Renormalization and wandering continua of rational maps
Guizhen Cui, Wenjuan Peng, Lei Tan
Renormalizations can be considered as building blocks of complex dynamical systems. This phenomenon has been widely studied for iterations of polynomials of one complex variable. C…