Unique ergodicity for random noninvertible maps on an interval

Key Points

• The aim is to explore conditions under which unique ergodicity occurs in noninvertible stochastic dynamical systems.
• Investigated noninvertible stochastic systems on the unit interval
• Provided conditions for unique ergodicity based on mean injectivity
• Presented specific examples demonstrating failure of unique ergodicity
• Established a condition for unique ergodicity in certain injective systems
• Identified cases where unique ergodicity does not hold

Abstract