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An open set of maps for which every point is absolutely nonshadowable. (English) Zbl 0996.37025
The goal of this paper is to discuss another mechanism for non-shadowability which the authors call “dimension variability”, that is, an attractor (with a dense trajectory) has at least two hyperbolic periodic orbits whose unstable manifolds have different dimensions. Using this phenomenon, the authors present an open set of maps (or diffeomorphisms) for which every point is absolutely nonshadowable. They also discuss geometrically how dimension variability is an obstacle for shadowing.

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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