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Journal Articles Nonlinearity Year : 2020

Typical properties of interval maps preserving the Lebesgue measure

Jozef Bobok
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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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Dates and versions

hal-02156804 , version 1 (14-06-2019)
hal-02156804 , version 2 (30-05-2020)

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Jozef Bobok, Serge Troubetzkoy. Typical properties of interval maps preserving the Lebesgue measure. Nonlinearity, 2020. ⟨hal-02156804v2⟩
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