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### Intermittency and regularized Fredholm determinants

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UNSPECIFIED.
(1999)
*Intermittency and regularized Fredholm determinants.*
INVENTIONES MATHEMATICAE, 135
(1).
pp. 1-24.
ISSN 0020-9910

**Full text not available from this repository.**

## Abstract

We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the associated Perron-Frobenius operator M has a continuous and residual spectrum contained in the line-segment sigma(c) = [0, 1] and a point spectrum sigma(p) which has no points of accumulation outside 0 and 1. Furthermore, points in sigma(p) - {0, 1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(lambda) which has a holomorphic extension to lambda epsilon C - sigma(c) and can be analytically continued from each side of a, to an open neighborhood of sigma(c) - {0, 1} (on different Riemann sheets). In C - sigma(c) the zero-set of d(lambda) is in one-to-one correspondence with the point spectrum of M. Through the conformal transformation lambda(z) = 1/4z (1 + z)(2) the function d o lambda(z) extends to a holomorphic function in a domain which contains the unit disc.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | INVENTIONES MATHEMATICAE |

Publisher: | SPRINGER VERLAG |

ISSN: | 0020-9910 |

Official Date: | January 1999 |

Volume: | 135 |

Number: | 1 |

Number of Pages: | 24 |

Page Range: | pp. 1-24 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/14979 |

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