Rotation number and dynamics of 3-interval piecewise λ -affine contractions
Abstract
Abstract We consider a family of piecewise contractions admitting a rotation number and defined for every x ∈ [ 0 , 1 ) by f ( x ) = λ x + δ + d θ a ( x ) ( mod 1 ) , where λ ∈ ( 0 , 1 ) , d ∈ ( 0 , 1 − λ ) , δ ∈ [ 0 , 1 ] , a ∈ [ 0 , 1 ] and θ a ( x ) = 1 if x ⩾ a and θ a ( x ) = 0 otherwise. In the special case where a = 1, the family reduces to the well studied ‘contracted rotations’ x ↦ λ x + δ ( mod 1 ) , which are 2-interval piecewise λ -affine contractions when δ ∈ ( 1 − λ , 1 ) . Considering
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
advanced mathematical theories
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 2
- Pages
- 025005–025005
- Publication date
- 6 February 2026