Existence of ACIM for Piecewise Expanding $C^{1+\varepsilon}$ maps
Existence of ACIM for Piecewise Expanding $C^{1+\varepsilon}$ maps
In this paper, we establish Lasota-Yorke inequality for the Frobenius-Perron Operator of a piecewise expanding $C^{1+\varepsilon}$ map of an interval. By adapting this inequality to satisfy the assumptions of the Ionescu-Tulcea and Marinescu ergodic theorem \cite{ionescu1950}, we demonstrate the existence of an absolutely continuous invariant measure (ACIM) for the map. …