Typical properties of interval maps preserving the Lebesgue measure
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 $(C(\lambda),\rho)$.
Domains
Dynamical Systems [math.DS]
Origin : Files produced by the author(s)