Displaying similar documents to “Periodic orbits with least period three on the circle.”

Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two

W. Ingram, Robert Roe (1999)

Colloquium Mathematicae

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We derive several properties of unimodal maps having only periodic points whose period is a power of 2. We then consider inverse limits on intervals using a single strongly unimodal bonding map having periodic points whose only periods are all the powers of 2. One such mapping is the logistic map, f λ ( x ) = 4λx(1-x) on [f(λ),λ], at the Feigenbaum limit, λ ≈ 0.89249. It is known that this map produces an hereditarily decomposable inverse limit with only three topologically different subcontinua....

Periodic segments and Nielsen numbers

Klaudiusz Wójcik (1999)

Banach Center Publications

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We prove that the Poincaré map φ ( 0 , T ) has at least N ( h ˜ , c l ( W 0 W 0 - ) ) fixed points (whose trajectories are contained inside the segment W) where the homeomorphism h ˜ is given by the segment W.

Periods and entropy for Lorenz-like maps

Lluis Alsedà, J. Llibre, M. Misiurewicz, C. Tresser (1989)

Annales de l'institut Fourier

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We characterize the set of periods and its structure for the Lorenz-like maps depending on the rotation interval. Also, for these maps we give the best lower bound of the topological entropy as a function of the rotation interval.

Applications of Nielsen theory to dynamics

Boju Jiang (1999)

Banach Center Publications

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In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.