Piecewise Expanding Maps and Conjugacy Equations

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 112)


Topological invariants of interval maps are preserved by conjugacy. We investigate some features of the conjugacy equations associated to piecewise expanding maps. For special cases, it is possible to construct explicitly a conjugacy function in terms of the a-base expansion of numbers through a solution of the corresponding functional equations.


Explicit Solution Gambler Playing Piecewise Continuous Function Expansivity Condition Conjugacy Equation 
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The first author acknowledges support by Fundação para a Ciência e Tecnologia, grant SFRH/BD/77623/2011. The second author acknowledges partial support by Fundação para a Ciência e Tecnologia, PEst-OE/MAT/UI0209/2013. The authors are also indebted to the anonymous referees for their sharp suggestions.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Centro de Matemática e Aplicações Fundamentais, Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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