Physics
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995nyasa.773..242w&link_type=abstract
Annals of the New York Academy of Sciences, vol. 773, issue 1, pp. 242-255
Physics
Stellar Dynamics: Chaos
Scientific paper
Results from both the Hénon map and the standard map support the claim that systems that include dynamical noise can be shadowed for long times for most orbits, provided that the noise amplitude δ is small enough. However, the existence of orbits with appreciably shorter shadowing times should cause concern when integrating chaotic dynamical systems for long times. The existence of these "unshadowable" orbits makes conclusions about the "shadowability" of orbits in a nonhyperbolic system unclear, even though the mean shadowing time may be quite large. This is especially true considering the fractal nature of the sample distributions of shadowing times. If one is interested in the shadowing time for an orbit with a certain initial condition, one has to realize that there are orbits with initial conditions arbitrarily close to the desired initial condition with drastically different shadowing times.
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