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Characterization of hyperbolicity and generalized shadowing lemma
Hyperbolicity Lyapunov exponents shadowing Anosov maps
2011/9/13
Abstract: J. Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle o...
Aggressive shadowing of a low-dimensional model of atmospheric dynamics
shadowing stalking ensemble forecasting inflation
2011/7/6
Predictions of the future state of the Earth's atmosphere suffer from the consequences of chaos: numerical weather forecast models quickly diverge from observations as uncertainty in the initial state...
Shadowing, expansiveness and stability of divergence-free vector fields
divergence-free vector fields math
2010/11/22
Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions:
1. X is in the C1-interior of th...
Shadowing and Inverse Shadowing for $C^1$ Endomorphisms
shadowing property inverse shadowing endomorphism Hyperbolic set
2007/12/10
In this paper, we consider the shadowing and the inverse shadowing properties for $C^{1}$ endomorphisms. We show that near a hyperbolic set a $C^{1}$ endomorphism has the shadowing property, and a hyp...