Rotation numbers, twists and a Sharkovskii–Misiurewicz-type ordering for patterns on the interval

DOI10.1017/S014338570000821XzbMath0842.58018MaRDI QIDQ4324890

Alexander M. Blokh

Publication date: 12 August 1996

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

rotation numberinterval mapsSharkovskij theorem

Mathematics Subject Classification ID

Low-dimensional dynamical systems (37E99)

Related Items (16)

Forcing among patterns with no block structure ⋮ The strongly simple cycles with given rotation pairs of an interval map ⋮ Entropy of twist interval maps ⋮ Forcing relation on patterns of invariant sets and reductions of interval maps ⋮ Turbulences and strict return trajectory types of interval mappings ⋮ Stability of rotation pairs of cycles for the interval maps ⋮ Rotation numbers for certain maps of an \(n\)-od ⋮ On Graph-realizable Sets of Periods ⋮ Functional Rotation Numbers for One-Dimensional Maps ⋮ MULTIDIMENSIONAL PERTURBATIONS OF ONE-DIMENSIONAL MAPS AND STABILITY OF SARKOVSKĬ ORDERING ⋮ Over-rotation intervals of bimodal interval maps ⋮ Monotonicity of the over-rotation interval for bimodal maps ⋮ Renormalization towers and their forcing ⋮ Recurrent and periodic points in dendritic Julia sets ⋮ Over-rotation numbers for unimodal maps ⋮ Rotating an interval and a circle

Cites Work

• Bifurcations and stability of families of diffeomorphisms
• Generalizations of a theorem of Šarkovskii on orbits of continuous real-valued functions
• Decomposition of dynamical systems on an interval
• Rotation Sets for Maps of Tori
• No Division Implies Chaos

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