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Fixed point theorems and their applications / / Ioannis Farmakis, Martin Moskowitz, City University of New York, USA
| Fixed point theorems and their applications / / Ioannis Farmakis, Martin Moskowitz, City University of New York, USA |
| Autore | Farmakis Ioannis |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2013] |
| Descrizione fisica | 1 online resource (xi, 234 pages) : illustrations |
| Disciplina | 515.7248 |
| Collana | Gale eBooks |
| Soggetto topico | Fixed point theory |
| ISBN | 981-4458-92-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface and Acknowledgments; Introduction; 1 Early Fixed Point Theorems; 1.1 The Picard-Banach Theorem; 1.2 Vector Fields on Spheres; 1.3 Proof of the Brouwer Theorem and Corollaries; 1.3.1 A Counter Example; 1.3.2 Applications of the Brouwer Theorem; 1.3.3 The Perron-Frobenius Theorem; 1.3.4 Google; A Billion Dollar Fixed Point Theorem; 1.4 Fixed Point Theorems for Groups of Affine Maps of Rn; 1.4.1 Affine Maps and Actions; 1.4.2 Affine Actions of Non Compact Groups; 2 Fixed Point Theorems in Analysis; 2.1 The Schauder-Tychonoff Theorem
2.1.1 Proof of the Schauder-Tychonoff Theorem2.2 Applications of the Schauder-Tychonoff Theorem; 2.3 The Theorems of Hahn, Kakutani and Markov-Kakutani; 2.4 Amenable Groups; 2.4.1 Amenable Groups; 2.4.2 Structure of Connected Amenable Lie Groups; 3 The Lefschetz Fixed Point Theorem; 3.1 The Lefschetz Theorem for Compact Polyhedra; 3.1.1 Projective Spaces; 3.2 The Lefschetz Theorem for a Compact Manifold; 3.2.1 Preliminaries from Differential Topology; 3.2.2 Transversality; 3.3 Proof of the Lefschetz Theorem; 3.4 Some Applications; 3.4.1 Maximal Tori in Compact Lie Groups 3.4.2 The Poincare-Hopf's Index Theorem3.5 The Atiyah-Bott Fixed Point Theorem; 3.5.1 The Case of the de Rham Complex; 4 Fixed Point Theorems in Geometry; 4.1 Some Generalities on Riemannian Manifolds; 4.2 Hadamard Manifolds and Cartan's Theorem; 4.3 Fixed Point Theorems for Compact Manifolds; 5 Fixed Points of Volume Preserving Maps; 5.1 The Poincare Recurrence Theorem; 5.2 Symplectic Geometry and its Fixed Point Theorems; 5.2.1 Introduction to Symplectic Geometry; 5.2.2 Fixed Points of Symplectomorphisms; 5.2.3 Arnold's Conjecture; 5.3 Poincare's Last Geometric Theorem 5.4 Automorphisms of Lie Algebras5.5 Hyperbolic Automorphisms of a Manifold; 5.5.1 The Case of a Torus; 5.5.2 Anosov Diffeomorphisms; 5.5.3 Nilmanifold Examples of Anosov Diffeomorphisms; 5.6 The Lefschetz Zeta Function; 6 Borel's Fixed Point Theorem in Algebraic Groups; 6.1 Complete Varieties and Borel's Theorem; 6.2 The Projective and Grassmann Spaces; 6.3 Projective Varieties; 6.4 Consequences of Borel's Fixed Point Theorem; 6.5 Two Conjugacy Theorems for Real Linear Lie Groups; 7 Miscellaneous Fixed Point Theorems; 7.1 Applications to Number Theory; 7.1.1 The Little Fermat Theorem 7.1.2 Fermat's Two Squares Theorem7.2 Fixed Points in Group Theory; 7.3 A Fixed Point Theorem in Complex Analysis; 8 A Fixed Point Theorem in Set Theory; Afterword; Bibliography; Index |
| Record Nr. | UNINA-9910790684903321 |
Farmakis Ioannis
|
||
| New Jersey : , : World Scientific, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fixed point theorems and their applications / / Ioannis Farmakis, Martin Moskowitz, City University of New York, USA
| Fixed point theorems and their applications / / Ioannis Farmakis, Martin Moskowitz, City University of New York, USA |
| Autore | Farmakis Ioannis |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2013] |
| Descrizione fisica | 1 online resource (xi, 234 pages) : illustrations |
| Disciplina | 515.7248 |
| Collana | Gale eBooks |
| Soggetto topico | Fixed point theory |
| ISBN | 981-4458-92-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface and Acknowledgments; Introduction; 1 Early Fixed Point Theorems; 1.1 The Picard-Banach Theorem; 1.2 Vector Fields on Spheres; 1.3 Proof of the Brouwer Theorem and Corollaries; 1.3.1 A Counter Example; 1.3.2 Applications of the Brouwer Theorem; 1.3.3 The Perron-Frobenius Theorem; 1.3.4 Google; A Billion Dollar Fixed Point Theorem; 1.4 Fixed Point Theorems for Groups of Affine Maps of Rn; 1.4.1 Affine Maps and Actions; 1.4.2 Affine Actions of Non Compact Groups; 2 Fixed Point Theorems in Analysis; 2.1 The Schauder-Tychonoff Theorem
2.1.1 Proof of the Schauder-Tychonoff Theorem2.2 Applications of the Schauder-Tychonoff Theorem; 2.3 The Theorems of Hahn, Kakutani and Markov-Kakutani; 2.4 Amenable Groups; 2.4.1 Amenable Groups; 2.4.2 Structure of Connected Amenable Lie Groups; 3 The Lefschetz Fixed Point Theorem; 3.1 The Lefschetz Theorem for Compact Polyhedra; 3.1.1 Projective Spaces; 3.2 The Lefschetz Theorem for a Compact Manifold; 3.2.1 Preliminaries from Differential Topology; 3.2.2 Transversality; 3.3 Proof of the Lefschetz Theorem; 3.4 Some Applications; 3.4.1 Maximal Tori in Compact Lie Groups 3.4.2 The Poincare-Hopf's Index Theorem3.5 The Atiyah-Bott Fixed Point Theorem; 3.5.1 The Case of the de Rham Complex; 4 Fixed Point Theorems in Geometry; 4.1 Some Generalities on Riemannian Manifolds; 4.2 Hadamard Manifolds and Cartan's Theorem; 4.3 Fixed Point Theorems for Compact Manifolds; 5 Fixed Points of Volume Preserving Maps; 5.1 The Poincare Recurrence Theorem; 5.2 Symplectic Geometry and its Fixed Point Theorems; 5.2.1 Introduction to Symplectic Geometry; 5.2.2 Fixed Points of Symplectomorphisms; 5.2.3 Arnold's Conjecture; 5.3 Poincare's Last Geometric Theorem 5.4 Automorphisms of Lie Algebras5.5 Hyperbolic Automorphisms of a Manifold; 5.5.1 The Case of a Torus; 5.5.2 Anosov Diffeomorphisms; 5.5.3 Nilmanifold Examples of Anosov Diffeomorphisms; 5.6 The Lefschetz Zeta Function; 6 Borel's Fixed Point Theorem in Algebraic Groups; 6.1 Complete Varieties and Borel's Theorem; 6.2 The Projective and Grassmann Spaces; 6.3 Projective Varieties; 6.4 Consequences of Borel's Fixed Point Theorem; 6.5 Two Conjugacy Theorems for Real Linear Lie Groups; 7 Miscellaneous Fixed Point Theorems; 7.1 Applications to Number Theory; 7.1.1 The Little Fermat Theorem 7.1.2 Fermat's Two Squares Theorem7.2 Fixed Points in Group Theory; 7.3 A Fixed Point Theorem in Complex Analysis; 8 A Fixed Point Theorem in Set Theory; Afterword; Bibliography; Index |
| Record Nr. | UNINA-9910814096803321 |
|
Farmakis Ioannis
|
||
| New Jersey : , : World Scientific, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||