The Dynamics of a Family of One-Dimensional Maps

Invariant densities for generalizedβ-maps

“…This It satisfies condition (6) but does not correspond to an itinerary of 1 for any β ∈ [1,2]. and equation (16) has β = 1 as a unique solution in [1,2]. Again, this It satisfies condition (6) but does not correspond to an itinerary of 1 for any β ∈ [1,2].…”

“…and equation (16) has β = 1 as a unique solution in [1,2]. This It satisfies condition (6) but does not correspond to an itinerary of 1 for any β ∈ [1,2].…”

“…Again, for the same β and E, if α < 2 − β, the system has an attracting basin [0, 1 − α] and τ |[0,1−α] is conjugated to τ β with vectorĒ = [1,0]. The invariant density can be found by conjugation or by the formula…”

“…It (1) ≤ It (2) if and only if the corresponding β satisfy β 1 ≤ β 2 . It (1) ≤ It (2) if and only if the corresponding β satisfy β 1 ≤ β 2 .…”

“…In [1] and [2] the authors studied the ergodic properties of 'skewed' tent maps. In [1] and [2] the authors studied the ergodic properties of 'skewed' tent maps.…”