Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors
Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in ter...
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1997 |
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| Umfang: |
20 |
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Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Communications in mathematical physics - 1965, 190(1997) vom: Feb., Seite 375-394 |
| Übergeordnetes Werk: |
volume:190 ; year:1997 ; month:02 ; pages:375-394 ; extent:20 |
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| 520 | |a Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire | ||
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(DE-627)NLEJ202210707 DE-627 ger DE-627 rakwb eng Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors 1997 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Communications in mathematical physics 1965 190(1997) vom: Feb., Seite 375-394 (DE-627)NLEJ188990305 (DE-600)1458931-x 1432-0916 nnns volume:190 year:1997 month:02 pages:375-394 extent:20 http://dx.doi.org/10.1007/s002200050245 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 190 1997 2 375-394 20 |
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(DE-627)NLEJ202210707 DE-627 ger DE-627 rakwb eng Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors 1997 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Communications in mathematical physics 1965 190(1997) vom: Feb., Seite 375-394 (DE-627)NLEJ188990305 (DE-600)1458931-x 1432-0916 nnns volume:190 year:1997 month:02 pages:375-394 extent:20 http://dx.doi.org/10.1007/s002200050245 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 190 1997 2 375-394 20 |
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(DE-627)NLEJ202210707 DE-627 ger DE-627 rakwb eng Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors 1997 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Communications in mathematical physics 1965 190(1997) vom: Feb., Seite 375-394 (DE-627)NLEJ188990305 (DE-600)1458931-x 1432-0916 nnns volume:190 year:1997 month:02 pages:375-394 extent:20 http://dx.doi.org/10.1007/s002200050245 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 190 1997 2 375-394 20 |
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(DE-627)NLEJ202210707 DE-627 ger DE-627 rakwb eng Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors 1997 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Communications in mathematical physics 1965 190(1997) vom: Feb., Seite 375-394 (DE-627)NLEJ188990305 (DE-600)1458931-x 1432-0916 nnns volume:190 year:1997 month:02 pages:375-394 extent:20 http://dx.doi.org/10.1007/s002200050245 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 190 1997 2 375-394 20 |
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Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors |
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Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire |
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Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire |
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Abstract: We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire |
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