Titlebook: Dynamics of One-Dimensional Maps; A. N. Sharkovsky,S. F. Kolyada,V. V. Fedorenko Book 1997 Springer Science+Business Media Dordrecht 1997

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The phase space of dynamical systems under consideration, i.e., the interval ., is endowed with Lebesgue measure. It is thus useful to establish some properties of dynamical systems that are typical with respect to this measure, i.e., properties exhibited by trajectories covering sets of full measure.

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Let . be a continuous map and let . = {β., β., ..., β.} be its cycle of period .≥1. One can distinguish between two types of stability of the cycle ., namely, between stability under perturbations of the initial data and stability under perturbations of the map. First, we consider the first type of stability.

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Elements of Symbolic Dynamics,Symbolic dynamics is a part of the general theory of dynamical systems dealing with cascades generated by shifts in various spaces of sequences . where θ. are letters of an alphabet . = {θ., θ., ..., θ.} The methods of symbolic dynamics are now widely applied to the investigation of various types of dynamical systems.

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Local Stability of Invariant Sets. Structural Stability of Unimodal Maps,Let . be a continuous map and let . = {β., β., ..., β.} be its cycle of period .≥1. One can distinguish between two types of stability of the cycle ., namely, between stability under perturbations of the initial data and stability under perturbations of the map. First, we consider the first type of stability.

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