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دسته بندی: ریاضیات ویرایش: نویسندگان: Bruno Scárdua سری: Latin American Mathematics Series ISBN (شابک) : 3030767043, 9783030767044 ناشر: Springer سال نشر: 2021 تعداد صفحات: 172 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 2 مگابایت
در صورت تبدیل فایل کتاب Holomorphic Foliations with Singularities: Key Concepts and Modern Results به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب شاخ و برگ های هولومورفیک با تکینگی ها: مفاهیم کلیدی و نتایج مدرن نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Preface Contents 1 The Classical Notions of Foliations 1.1 Definition of Foliation 1.2 Other Definitions of Foliation 1.3 Frobenius Theorem 1.4 Holonomy 1.5 Exercises 2 Some Results from Several Complex Variables 2.1 Some Extension Theorems from Several Complex Variables 2.2 Levi\'s Global Extension Theorem 2.3 Exercises 3 Holomorphic Foliations: Non-singular Case 3.1 Basic Concepts 3.2 Examples 3.3 The Identity Principle for Holomorphic Foliations 3.4 Exercises 4 Holomorphic Foliations with Singularities 4.1 Linear Vector Fields on the Plane 4.2 One-Dimensional Foliations with Isolated Singularities 4.3 Differential Forms and Vector Fields 4.4 Codimension One Foliations with Singularities 4.5 Analytic Leaves 4.6 Two Extension Lemmas for Holomorphic Foliations 4.7 Kupka Singularities and Simple Singularities 4.8 Exercises 5 Holomorphic Foliations Given by Closed 1-Forms 5.1 Foliations Given by Closed Holomorphic 1-Forms 5.1.1 Holonomy of Foliations Defined by Closed Holomorphic 1-Forms 5.2 Foliations Given by Closed Meromorphic 1-Forms 5.2.1 Holonomy of Foliations Defined by Closed meromorphic 1-Forms 5.3 Exercises 6 Reduction of Singularities 6.1 Irreducible Singularities 6.2 Poincaré and Poincaré–Dulac Normal Forms 6.3 Blow-up at the Origin (Quadratic Blow-up) 6.4 Blow-up on Surfaces 6.4.1 Resolution of Curves 6.5 Blow-up of a Singular Point of a Foliation 6.6 Irreducible Singularities 6.7 Separatrices: Dicriticalness and Existence 6.8 Holonomy and Analytic Classification 6.8.1 Holonomy of Irreducible Singularities 6.8.2 Holonomy and Analytic Classification of Irreducible Singularities 6.9 Examples 6.10 Exercises 7 Holomorphic First Integrals 7.1 Mattei–Moussu Theorem 7.2 Groups of Germs of Holomorphic Diffeomorphisms 7.3 Irreducible Singularities 7.4 The Case of a Single Blow-up 7.5 The General Case 7.6 Exercises 8 Dynamics of a Local Diffeomorphism 8.1 Hyperbolic Case 8.2 Parabolic Case 8.3 Elliptic Case 8.4 Exercises 9 Foliations on Complex Projective Spaces 9.1 The Complex Projective Plane and Foliations 9.2 The Theorem of Darboux–Jouanolou 9.3 Foliations Given by Closed 1-Forms 9.4 Riccati Foliations 9.5 Examples of Foliations on C P(2) 9.6 Example of an Action of a Low-dimensional Lie Algebra 9.7 A Family of Foliations on C P(3) Not Coming from Plane Foliations 9.8 Exercises 10 Foliations with Algebraic Limit Sets 10.1 Limit Sets of Foliations 10.2 Groups of Germs of Diffeomorphisms with Finite Limit Set 10.3 Virtual Holonomy Groups 10.4 Construction of Closed Meromorphic Forms 10.5 The Linearization Theorem 10.6 Examples 10.7 Exercises 11 Some Modern Questions 11.1 Holomorphic Flows on Stein Spaces 11.1.1 Suzuki\'s Theory 11.1.2 Proof of the Global Linearization Theorem 11.2 Real Transverse Sections of Holomorphic Foliations 11.3 Non-trivial Minimal Sets of Holomorphic Foliations 11.4 Transversely Homogeneous Holomorphic Foliations 11.4.1 Transversely Lie Foliations 11.5 Transversely Affine Foliations 11.6 Transversely Projective Foliations 11.6.1 Development of a Transversely Projective Foliation—Touzet\'s Work 11.6.2 Projective Structures and Differential Forms Proof of Proposition 11.6.5 Classification of Projective Foliations: Moderate Growth on Projective Manifolds 12 Miscellaneous Exercises and Some Open Questions 12.1 Miscellaneous Exercises 12.2 Some Open Questions Bibliography Index