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Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]]
| Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]] |
| Autore | Baake Michael |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xvi, 531 pages) : digital, PDF file(s) |
| Disciplina | 548.7 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Aperiodic tilings
Quasicrystals - Mathematics |
| ISBN |
1-316-18318-1
1-316-18367-X 1-316-18377-7 1-316-18448-X 1-316-18473-0 1-316-18403-X 1-139-02525-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Series information; Title page; Copyright information; Table of contents; Foreword; Preface; Chapter 1 Introduction; Chapter 2 Preliminaries; 2.1. Point sets; 2.2. Voronoi and Delone cells; 2.3. Groups; 2.4. Perron-Frobenius theory; 2.5. Number-theoretic tools; Chapter 3 Lattices and Crystals; 3.1. Periodicity and lattices; 3.2. The crystallographic restriction; 3.3. Root lattices; 3.4. Minkowski embedding; Chapter 4 Symbolic Substitutions and Inflations; 4.1. Substitution rules; 4.2. Hulls and their properties; 4.3. Symmetries, invariant measures and ergodicity
4.4. Metallic means sequences4.5. Period doubling and paper folding; 4.6. Thue-Morse substitution; 4.7. Rudin-Shapiro and Kolakoski sequences; 4.8. Complexity and further directions; 4.9. Block substitutions; Chapter 5 Patterns and Tilings; 5.1. Patterns and local indistinguishability; 5.2. Local derivability; 5.3. Repetitivity and finite local complexity; 5.4. Geometric hull; 5.5. Proximality; 5.6. Symmetry and inflation; 5.7. Local rules; Chapter 6 Inflation Tilings; 6.1. Ammann-Beenker tilings; 6.2. Penrose tilings and their relatives; 6.3. Square triangle and shield tilings 6.4. Planar tilings with integer inflation multiplier6.5. Examples of non-Pisot tilings; 6.6. Pinwheel tilings; 6.7. Tilings in higher dimensions; 6.8. Colourful examples; Chapter 7 Projection Method and Model Sets; 7.1. Silver mean chain via projection; 7.2. Cut and project schemes and model sets; 7.3. Cyclotomic model sets; 7.4. Icosahedral model sets and beyond; 7.5. Alternative constructions; Chapter 8 Fourier Analysis and Measures; 8.1. Fourier series; 8.2. Almost periodic functions; 8.3. Fourier transform of functions; 8.4. Fourier transform of distributions 8.5. Measures and their decomposition8.6. Fourier transform of measures; 8.7. Fourier-Stieltjes coefficients of measures on S1; 8.8. Volume averaged convolutions; Chapter 9 Diffraction; 9.1. Mathematical diffraction theory; 9.2. Poisson's summation formula and perfect crystals; 9.3. Autocorrelation and diffraction of the silver mean chain; 9.4. Autocorrelation and diffraction of regular model sets; 9.5. Pure point diffraction of weighted Dirac combs; 9.6. Homometric point sets; Chapter 10 Beyond Model Sets; 10.1. Diffraction of the Thue-Morse chain 10.2. Diffraction of the Rudin-Shapiro chain10.3. Diffraction of lattice subsets; 10.4. Visible lattice points; 10.5. Extension to Meyer sets; Chapter 11 Random Structures; 11.1. Probabilistic preliminaries; 11.2. Bernoulli systems; 11.3. Renewal processes on the line; 11.4. Point processes from random matrix theory; 11.5. Lattice systems with interaction; 11.6. Random tilings; Appendix A The Icosahedral Group; Appendix B The Dynamical Spectrum; References; List of Definitions; List of Examples; List of Remarks; Index |
| Record Nr. | UNINA-9910466882903321 |
Baake Michael
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]]
| Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]] |
| Autore | Baake Michael |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xvi, 531 pages) : digital, PDF file(s) |
| Disciplina | 548.7 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Aperiodic tilings
Quasicrystals - Mathematics |
| ISBN |
1-316-18318-1
1-316-18367-X 1-316-18377-7 1-316-18448-X 1-316-18473-0 1-316-18403-X 1-139-02525-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Series information; Title page; Copyright information; Table of contents; Foreword; Preface; Chapter 1 Introduction; Chapter 2 Preliminaries; 2.1. Point sets; 2.2. Voronoi and Delone cells; 2.3. Groups; 2.4. Perron-Frobenius theory; 2.5. Number-theoretic tools; Chapter 3 Lattices and Crystals; 3.1. Periodicity and lattices; 3.2. The crystallographic restriction; 3.3. Root lattices; 3.4. Minkowski embedding; Chapter 4 Symbolic Substitutions and Inflations; 4.1. Substitution rules; 4.2. Hulls and their properties; 4.3. Symmetries, invariant measures and ergodicity
4.4. Metallic means sequences4.5. Period doubling and paper folding; 4.6. Thue-Morse substitution; 4.7. Rudin-Shapiro and Kolakoski sequences; 4.8. Complexity and further directions; 4.9. Block substitutions; Chapter 5 Patterns and Tilings; 5.1. Patterns and local indistinguishability; 5.2. Local derivability; 5.3. Repetitivity and finite local complexity; 5.4. Geometric hull; 5.5. Proximality; 5.6. Symmetry and inflation; 5.7. Local rules; Chapter 6 Inflation Tilings; 6.1. Ammann-Beenker tilings; 6.2. Penrose tilings and their relatives; 6.3. Square triangle and shield tilings 6.4. Planar tilings with integer inflation multiplier6.5. Examples of non-Pisot tilings; 6.6. Pinwheel tilings; 6.7. Tilings in higher dimensions; 6.8. Colourful examples; Chapter 7 Projection Method and Model Sets; 7.1. Silver mean chain via projection; 7.2. Cut and project schemes and model sets; 7.3. Cyclotomic model sets; 7.4. Icosahedral model sets and beyond; 7.5. Alternative constructions; Chapter 8 Fourier Analysis and Measures; 8.1. Fourier series; 8.2. Almost periodic functions; 8.3. Fourier transform of functions; 8.4. Fourier transform of distributions 8.5. Measures and their decomposition8.6. Fourier transform of measures; 8.7. Fourier-Stieltjes coefficients of measures on S1; 8.8. Volume averaged convolutions; Chapter 9 Diffraction; 9.1. Mathematical diffraction theory; 9.2. Poisson's summation formula and perfect crystals; 9.3. Autocorrelation and diffraction of the silver mean chain; 9.4. Autocorrelation and diffraction of regular model sets; 9.5. Pure point diffraction of weighted Dirac combs; 9.6. Homometric point sets; Chapter 10 Beyond Model Sets; 10.1. Diffraction of the Thue-Morse chain 10.2. Diffraction of the Rudin-Shapiro chain10.3. Diffraction of lattice subsets; 10.4. Visible lattice points; 10.5. Extension to Meyer sets; Chapter 11 Random Structures; 11.1. Probabilistic preliminaries; 11.2. Bernoulli systems; 11.3. Renewal processes on the line; 11.4. Point processes from random matrix theory; 11.5. Lattice systems with interaction; 11.6. Random tilings; Appendix A The Icosahedral Group; Appendix B The Dynamical Spectrum; References; List of Definitions; List of Examples; List of Remarks; Index |
| Record Nr. | UNINA-9910795917503321 |
|
Baake Michael
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]]
| Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]] |
| Autore | Baake Michael |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xvi, 531 pages) : digital, PDF file(s) |
| Disciplina | 548.7 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Aperiodic tilings
Quasicrystals - Mathematics |
| ISBN |
1-316-18318-1
1-316-18367-X 1-316-18377-7 1-316-18448-X 1-316-18473-0 1-316-18403-X 1-139-02525-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Series information; Title page; Copyright information; Table of contents; Foreword; Preface; Chapter 1 Introduction; Chapter 2 Preliminaries; 2.1. Point sets; 2.2. Voronoi and Delone cells; 2.3. Groups; 2.4. Perron-Frobenius theory; 2.5. Number-theoretic tools; Chapter 3 Lattices and Crystals; 3.1. Periodicity and lattices; 3.2. The crystallographic restriction; 3.3. Root lattices; 3.4. Minkowski embedding; Chapter 4 Symbolic Substitutions and Inflations; 4.1. Substitution rules; 4.2. Hulls and their properties; 4.3. Symmetries, invariant measures and ergodicity
4.4. Metallic means sequences4.5. Period doubling and paper folding; 4.6. Thue-Morse substitution; 4.7. Rudin-Shapiro and Kolakoski sequences; 4.8. Complexity and further directions; 4.9. Block substitutions; Chapter 5 Patterns and Tilings; 5.1. Patterns and local indistinguishability; 5.2. Local derivability; 5.3. Repetitivity and finite local complexity; 5.4. Geometric hull; 5.5. Proximality; 5.6. Symmetry and inflation; 5.7. Local rules; Chapter 6 Inflation Tilings; 6.1. Ammann-Beenker tilings; 6.2. Penrose tilings and their relatives; 6.3. Square triangle and shield tilings 6.4. Planar tilings with integer inflation multiplier6.5. Examples of non-Pisot tilings; 6.6. Pinwheel tilings; 6.7. Tilings in higher dimensions; 6.8. Colourful examples; Chapter 7 Projection Method and Model Sets; 7.1. Silver mean chain via projection; 7.2. Cut and project schemes and model sets; 7.3. Cyclotomic model sets; 7.4. Icosahedral model sets and beyond; 7.5. Alternative constructions; Chapter 8 Fourier Analysis and Measures; 8.1. Fourier series; 8.2. Almost periodic functions; 8.3. Fourier transform of functions; 8.4. Fourier transform of distributions 8.5. Measures and their decomposition8.6. Fourier transform of measures; 8.7. Fourier-Stieltjes coefficients of measures on S1; 8.8. Volume averaged convolutions; Chapter 9 Diffraction; 9.1. Mathematical diffraction theory; 9.2. Poisson's summation formula and perfect crystals; 9.3. Autocorrelation and diffraction of the silver mean chain; 9.4. Autocorrelation and diffraction of regular model sets; 9.5. Pure point diffraction of weighted Dirac combs; 9.6. Homometric point sets; Chapter 10 Beyond Model Sets; 10.1. Diffraction of the Thue-Morse chain 10.2. Diffraction of the Rudin-Shapiro chain10.3. Diffraction of lattice subsets; 10.4. Visible lattice points; 10.5. Extension to Meyer sets; Chapter 11 Random Structures; 11.1. Probabilistic preliminaries; 11.2. Bernoulli systems; 11.3. Renewal processes on the line; 11.4. Point processes from random matrix theory; 11.5. Lattice systems with interaction; 11.6. Random tilings; Appendix A The Icosahedral Group; Appendix B The Dynamical Spectrum; References; List of Definitions; List of Examples; List of Remarks; Index |
| Record Nr. | UNINA-9910828054403321 |
|
Baake Michael
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
