Parrondo’s Paradox for Tent Maps

Abstract

In this paper, we study the dynamic Parrondo’s paradox for the well-known family of tent maps. We prove that this paradox is impossible when we consider piecewise linear maps with constant slope. In addition, we analyze the paradox “simple + simple = complex” when a tent map with constant slope and a piecewise linear homeomorphism with two different slopes are considered.

Keywords

• Parrondo’s paradox
• tent maps
• topological entropy
• piecewise linear maps