Constant Slope Models and Perturbation
Michal Malek, Samuel Roth
TL;DR
This paper improves the understanding of how preimages grow under certain interval maps and examines the stability of the constant slope model operator.
Contribution
It provides a sharper estimate for preimage growth rates and analyzes the continuity of the constant slope model operator for transitive piecewise monotone interval maps.
Findings
Enhanced estimate for preimage growth rate.
Continuity results for the constant slope model operator.
Application to transitive piecewise monotone maps.
Abstract
We sharpen an estimate for the growth rate of preimages of a point under a transitive piecewise monotone interval map. Then we apply our estimate to study the continuity of the operator which assigns to such a map its constant slope model.
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