### Abstract

We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

Original language | English |
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Pages (from-to) | 1927-1930 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 73 |

Issue number | 14 |

Publication status | Published - 3 Oct 1994 |

### Keywords

- DYNAMIC-SYSTEMS
- TRAJECTORIES

## Cite this

DAWSON, S., GREBOGI, C., SAUER, T., & YORKE, J. A. (1994). OBSTRUCTIONS TO SHADOWING WHEN A LYAPUNOV EXPONENT FLUCTUATES ABOUT ZERO.

*Physical Review Letters*,*73*(14), 1927-1930.