Decay of correlations and memory loss for Lasota–Yorke convex maps

Abstract

For a class of piecewise convex maps f on the interval $[0,1]$, we show that f has a unique absolutely continuous invariant probability measure μ with exponential decay of correlations, and we also present the explicit upper bounds on the rate. Moreover, we show the exponential loss of memory for a sequential dynamical system consisting of piecewise convex maps.

Keywords:

• Lasota–Yorke convex
• memory loss
• decay of correlations

2010 Mathematics Subject Classifications:

• 37E05
• 37C40

Acknowledgments

The author is very grateful to the referee for thorough reading and helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant No. 11671395].