For every fixed attracting multiplier ρ, the λ-parameter slice of this exponential-based meromorphic family divides into two connected full sets Mλ, Mμ and a shift locus S conformally equivalent to a punctured annulus.
Monotonicity of entropy and positively oriented transversality for families of interval maps
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abstract
In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain transversality for a wide class of one-parameter families of interval maps, for example maps with flat critical points, piecewise linear maps, maps with discontinuities but also for families of maps with complex analytic extensions such as certain polynomial-like maps.
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Slices of Parameter Space for Meromorphic Maps with Two Asymptotic Values
For every fixed attracting multiplier ρ, the λ-parameter slice of this exponential-based meromorphic family divides into two connected full sets Mλ, Mμ and a shift locus S conformally equivalent to a punctured annulus.