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:''A Shadowing lemma is also a fictional creature in the Discworld. See Shadowing lemma.'' In the theory of dynamical systems, the shadowing lemma is a lemma describing the behaviour of pseudo-orbits near a hyperbolic invariant set. Informally, the theory states that every pseudo-orbit (which one can think of as a numerically computed trajectory with rounding errors on every step) stays uniformly close to some true trajectory (with slightly altered initial position) — in other words, a pseudo-trajectory is "shadowed" by a true one. Incapability of the shadowing lemma on digital chaos are presented in the International Journal of Bifurcation and Chaos, Sec. 2.2.3. == Formal statement == Given a map ''f'' : ''X'' → ''X'' of a metric space (''X'', ''d'') to itself, define a ε-pseudo-orbit (or ε-orbit) as a sequence of points such that belongs to a ε-neighborhood of . Then, near a hyperbolic invariant set, the following statement holds:〔A. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems, Theorem 18.1.2.〕 Let Λ be a hyperbolic invariant set of a diffeomorphism f. There exists a neighborhood U of Λ with the following property: for any ''δ'' > 0 there exists ''ε'' > 0, such that any (finite or infinite) ε-pseudo-orbit that stays in U also stays in a δ-neighborhood of some true orbit. : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Shadowing lemma」の詳細全文を読む スポンサード リンク
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