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arXiv · 1906.07558

Typical properties of interval maps preserving the Lebesgue measure

Jozef Bobok·Serge Troubetzkoy
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Abstract

Let us denote $\lambda$ the Lebesgue measure on $[0,1]$, put$$ C(\lambda)=\{f\in C([0,1]);\ \forall~A\subset [0,1], A~\text{Borel}:\ \lambda(A)=\lambda(f^{-1}(A))\}.$$ We endow the set $C(\lambda)$ by the uniform metric $\rho$ and investigate dynamical properties of typical maps in the complete metric space $(C(\lambda),\rho)$.

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Jozef Bobok, Serge Troubetzkoy. 2019-06-18. Typical properties of interval maps preserving the Lebesgue measure. https://doi.org/10.1088/1361-6544/aba5e6

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