Intermittency and regularized Fredholm determinants
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 σ c =[0,1] a...
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Umfang: |
24 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Inventiones mathematicae - 1966, 135(1999) vom: Jan., Seite 1-24 |
| Übergeordnetes Werk: |
volume:135 ; year:1999 ; month:01 ; pages:1-24 ; extent:24 |
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| 520 | |a 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. | ||
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(DE-627)NLEJ202319032 DE-627 ger DE-627 rakwb eng Intermittency and regularized Fredholm determinants 1999 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. Springer Online Journal Archives 1860-2002 Rugh, Hans Henrik oth in Inventiones mathematicae 1966 135(1999) vom: Jan., Seite 1-24 (DE-627)NLEJ188991883 (DE-600)1398341-6 1432-1297 nnns volume:135 year:1999 month:01 pages:1-24 extent:24 http://dx.doi.org/10.1007/s002220050277 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 135 1999 1 1-24 24 |
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(DE-627)NLEJ202319032 DE-627 ger DE-627 rakwb eng Intermittency and regularized Fredholm determinants 1999 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. Springer Online Journal Archives 1860-2002 Rugh, Hans Henrik oth in Inventiones mathematicae 1966 135(1999) vom: Jan., Seite 1-24 (DE-627)NLEJ188991883 (DE-600)1398341-6 1432-1297 nnns volume:135 year:1999 month:01 pages:1-24 extent:24 http://dx.doi.org/10.1007/s002220050277 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 135 1999 1 1-24 24 |
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(DE-627)NLEJ202319032 DE-627 ger DE-627 rakwb eng Intermittency and regularized Fredholm determinants 1999 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. Springer Online Journal Archives 1860-2002 Rugh, Hans Henrik oth in Inventiones mathematicae 1966 135(1999) vom: Jan., Seite 1-24 (DE-627)NLEJ188991883 (DE-600)1398341-6 1432-1297 nnns volume:135 year:1999 month:01 pages:1-24 extent:24 http://dx.doi.org/10.1007/s002220050277 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 135 1999 1 1-24 24 |
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(DE-627)NLEJ202319032 DE-627 ger DE-627 rakwb eng Intermittency and regularized Fredholm determinants 1999 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. Springer Online Journal Archives 1860-2002 Rugh, Hans Henrik oth in Inventiones mathematicae 1966 135(1999) vom: Jan., Seite 1-24 (DE-627)NLEJ188991883 (DE-600)1398341-6 1432-1297 nnns volume:135 year:1999 month:01 pages:1-24 extent:24 http://dx.doi.org/10.1007/s002220050277 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 135 1999 1 1-24 24 |
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(DE-627)NLEJ202319032 DE-627 ger DE-627 rakwb eng Intermittency and regularized Fredholm determinants 1999 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier 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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. Springer Online Journal Archives 1860-2002 Rugh, Hans Henrik oth in Inventiones mathematicae 1966 135(1999) vom: Jan., Seite 1-24 (DE-627)NLEJ188991883 (DE-600)1398341-6 1432-1297 nnns volume:135 year:1999 month:01 pages:1-24 extent:24 http://dx.doi.org/10.1007/s002220050277 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 135 1999 1 1-24 24 |
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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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. |
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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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. |
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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 σ c =[0,1] and a point spectrum σ p which has no points of accumulation outside 0 and 1. Furthermore, points in σ p −{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ c and can be analytically continued from each side of σ c to an open neighborhood of σ c −{0,1} (on different Riemann sheets). In ℂ−σ c the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc. |
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