scholarly journals Shadowing lemma for flows

Scholarpedia ◽  
2009 ◽  
Vol 4 (4) ◽  
pp. 7918 ◽  
Author(s):  
Kenneth Palmer
Keyword(s):  
Shadowing Lemma

scholarly journals Chaos and shadowing around a homoclinic tube

2003 ◽  
Vol 2003 (16) ◽  
pp. 923-931 ◽  
Author(s):  
Yanguang (Charles) Li
Keyword(s):  
Banach Space ◽  
Invariant Manifold ◽  
Bernoulli Shift ◽  
Current Work ◽  
Shadowing Lemma ◽  
Shift Dynamics

LetFbe aC3diffeomorphism on a Banach spaceB.Fhas a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable condition of Silnikov (1968). Also, the result of Silnikov does not imply Bernoulli shift dynamics of a single map, but rather only provides a labeling of all invariant tubes around the homoclinic tube. The work of Silnikov was done inℝnand the current work is done in a Banach space.

scholarly journals A shadowing lemma for quasi-hyperbolic strings of flows

2018 ◽  
Vol 264 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Bo Han ◽  
Xiao Wen
Keyword(s):  
Shadowing Lemma

BENFORD'S LAW IN POWER-LIKE DYNAMICAL SYSTEMS

2005 ◽  
Vol 05 (04) ◽  
pp. 587-607 ◽  
Author(s):  
ARNO BERGER
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Benford’S Law ◽  
Regularity Conditions ◽  
Stochastic Dynamical Systems ◽  
Shadowing Lemma ◽  
Contraction Condition ◽  
The Family ◽  
Benford's Law ◽  
Almost All

A generalized shadowing lemma is used to study the generation of Benford sequences under non-autonomous iteration of power-like maps Tj : x ↦ αjxβj (1 - fj(x)), with αj, βj > 0 and fj ∈ C1, fj(0) = 0, near the fixed point at x = 0. Under mild regularity conditions almost all orbits close to the fixed point asymptotically exhibit Benford's logarithmic mantissa distribution with respect to all bases, provided that the family (Tj) is contracting on average, i.e. [Formula: see text]. The technique presented here also applies if the maps are chosen at random, in which case the contraction condition reads 𝔼 log β > 0. These results complement, unify and widely extend previous work. Also, they supplement recent empirical observations in experiments with and simulations of deterministic as well as stochastic dynamical systems.

scholarly journals A generalized shadowing lemma

2002 ◽  
Vol 8 (3) ◽  
pp. 627-632 ◽  
Author(s):  
Shaobo Gan ◽  
Keyword(s):  
Shadowing Lemma

scholarly journals Transition map and shadowing lemma for normally hyperbolic invariant manifolds

2013 ◽  
Vol 33 (3) ◽  
pp. 1089-1112 ◽  
Author(s):  
Amadeu Delshams ◽  
◽  
Marian Gidea ◽  
Pablo Roldán ◽  
◽  
...  
Keyword(s):  
Invariant Manifolds ◽  
Shadowing Lemma ◽  
Transition Map ◽  
Normally Hyperbolic Invariant Manifolds

scholarly journals Characterization of hyperbolicity and generalized shadowing lemma

2011 ◽  
Vol 26 (4) ◽  
pp. 483-502 ◽  
Author(s):  
Davor Dragičević ◽  
Siniša Slijepčević
Keyword(s):  
Shadowing Lemma
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