Explicit dynamical systems on the Sierpinski carpet

We apply Boroniski and Oprocha's inverse limit construction of dynamical systems on the Sierpiniski carpet by using the initial systems of n-Chamanara surfaces and their n -baker transformations, n >= 2. We show that all positive real numbers are realized as metric entropy values of dynamical systems on the carpet. We also produce a simplification of Boroniski and Oprocha's proof showing that dynamical systems on the carpet do not have the Bowen specification property. (c) 2024 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.