# pseudo-orbit

Let $(X,d)$ be a metric space, $f:X\to X$ a function, and let $\u03f5>0$. An $\u03f5$-pseudo-orbit for $f$ is a sequence $$, where $$, such that $$ for all $$. A periodic pseudo-orbit is an infinite pseudo-orbit $\{{x}_{n}\}$ such that there is some $p$ with ${x}_{n+p}={x}_{n}$ for all n.

Given $\delta >0$, the pseudo-orbit $$ is said to be $\delta $-shadowed by the orbit of $x$, if $$ for all $$.

Title | pseudo-orbit |
---|---|

Canonical name | Pseudoorbit |

Date of creation | 2013-03-22 14:07:19 |

Last modified on | 2013-03-22 14:07:19 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 7 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 37C50 |

Synonym | pseudo orbit |

Synonym | $\u03f5$-pseudo-orbit |

Synonym | $\u03f5$-orbit |

Synonym | $\u03f5$-chain |

Defines | shadow |

Defines | shadowing |

Defines | shadowed |