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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.
In this paper we will develop a general approach which shows that generalized critical relations of families of locally defined holomorphic maps on the complex plane unfold transversally. The main idea is to define a transfer operator, which is a loc
In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps.
We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves in the mo
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the critical orbit
We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.