Computing Invariant Densities of a Class of Piecewise

Document Type

Article

Publication Date

4-1-2023

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Let S : [0, 1] → [0, 1] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.

Publication Title

International Journal of Bifurcation and Chaos

Volume

33

Issue

5

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