Shadowing in Dynamical Systems

By K. Palmer. 2000

657 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fc68a48aef7274016f3e183db21d8c1e6f6a2b59

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Citations in the corpus

Shadowing for actions of some finitely generated groups (2013, background): “Theory of shadowing is now a sufficiently well-developed branch of theory of dynamical systems (see monographs [1, 2] and a review of modern results [3]).”
N-expansive homeomorphisms with the shadowing property (2016, background): “This property was extensively studied due to its relation to the hyperbolic and stability thoeries (see [2], [14]).”
Generic Morse-Smale property for the parabolic equation on the circle (2010, neutral): “For additional references, see [12], [43], [44], [45], [19] and [53] for example.”
A General Approximation Scheme for Attractors of Abstract Parabolic Problems (2006, positive): “Pilyugin (1999).”
Gradients are Not All You Need (2021, background): “To do this they take advantage of the shadowing lemma[Pilyugin, 2006].”
Continuous inverse shadowing and hyperbolicity (2003, background): “Notions of shadowing, coordinates, expansiveness and the like have been to be useful for this purpose (see [3, 4, 9, 11, 12]).”
Anosov flows and dynamical zeta functions (2012, positive): “se. First of all we deﬁne the (ε0,T)-pseudo-orbits t(t) : R → M to be a map such that for any t′ ∈ Rwe have d(φ t(t(t′)),t(t+t′)) ≤ ε0 if |t| <T.41 Then we have the following theorem. Theorem 5.2 ([40]). Let Mbe a smooth manifold and φt a C2 Anosov ﬂow. There exists ε0 >0,C3 ≥ 1 such that give”
Shadowable points (2015, methodology): “Proof: Define X = C [1, 2] with the topology induced from R, where C be the ternary Cantor set of [0, 1].”
Sets of Dynamical Systems with Various Limit Shadowing Properties (2007, methodology): “It was noted in [ 1 ] that a diffeomorphism has the TSLmSP in a neighborhood of a hyperbolic set.”
On homeomorphisms with the two-sided limit shadowing property (2014, background): “Excellent references for the shadowing property are Pilyugin’s book [12] and Aoki and Hiraide’s monograph [1].”
A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers (2014, background): “Let us mention yet that the problem of Hyers-Ulam stability of functional equations is connected to the notions of controlled chaos (see [31]) and shadowing (see [11, 25, 27]).”