TY - JOUR

T1 - Approximate and Real Trajectories for Generic Dynamical Systems

AU - Corless, Robert M.

AU - Pilyugin, S. Yu

PY - 1995/1/15

Y1 - 1995/1/15

N2 - In this paper we show that generic dynamical systems have a weak shadowing property, namely that for a generic dynamical system φ, in the space of discrete continuous dynamical systems on a compact manifold M with the usual C0 topology, given ε{lunate} > 0, there exists a δ > 0 such that δ-trajectories are ε{lunate}-close to real trajectories. There are no dimensional restrictions on this result. We also give some results on the "inverse" problem of tracing real trajectories by δ-trajectories. These problems are motivated by questions regarding the validity of numerical solutions of differential equations.

AB - In this paper we show that generic dynamical systems have a weak shadowing property, namely that for a generic dynamical system φ, in the space of discrete continuous dynamical systems on a compact manifold M with the usual C0 topology, given ε{lunate} > 0, there exists a δ > 0 such that δ-trajectories are ε{lunate}-close to real trajectories. There are no dimensional restrictions on this result. We also give some results on the "inverse" problem of tracing real trajectories by δ-trajectories. These problems are motivated by questions regarding the validity of numerical solutions of differential equations.

UR - http://www.scopus.com/inward/record.url?scp=0000539586&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1995.1027

DO - 10.1006/jmaa.1995.1027

M3 - Article

AN - SCOPUS:0000539586

VL - 189

SP - 409

EP - 423

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -