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• W285127579 abstract "1 Definitions and Examples: Preliminaries Basic constructions Basic examples. 2 Poncare-Bendixon's theory: Existence of closed transversal Absence of non-trivial recurrent trajectories on some surfaces Hilmy's and Cherry's theorems on quasiminimal sets Gutierrez's structure theorem Limit set of individual trajectory 3 Decomposition of flows: Decomposition theorems Center of flow Blowing-down of flows Regular flows Application: smoothing of flows. 4 Local Theory: Topological normal forms Analytical normal forms Smooth normal forms Finitely smooth normal forms, Degenerate critical points C1 normal forms of degenerate singularities. 5 Space of Flows and vector fields: Structural stability Classification of Morse-Smale flows Lyapunov's method, Connected components of Morse-Smale flows Degrees of non-stability, Typical properties of non-stable flows. 6 Ergodic theory: Liouville's theorem Kolmogorov's theorem for flows on torus Non-trivial invariant measures Ergodicity Mixing Entropy. 7 Invariants of surface flows: Topological classification of torus flows Oriented surfaces of higher genus .z 2 Application of geodesic laminations Transitive flows on non-orientable surfaces Classification of exceptional minimal sets Classification of regular flows Classification of non-wandering flows Cayley graph of a flow Homology and cohomology invariants Rotation sets of surface flows Smooth classification of flows. 8 C*-algebras of Surface Flows: Irrational rotation algebra Artin's rotation algebra K-theory C*-algebra of Morse-Smale flows. 9 Semi-local Theory: Denjoy's and Schwarz's theorems Cherry's problem Local structure preventing quasiminimality. 10 Anosov-Weil Problem: Theorems of Weil and Anosov Asymptotic direction of individual curves Approximation of curve by trajectories of a flow Limit sets of curves and trajectories at the absolute Deviation of curves from the geodesics Examples of unbounded deviation. 11 Non-compact Surfaces: Kaplan classification Level curves of harmonic functions Markus's classification Structural stability Neumann's example Inaba example and Beniere-Meigniez theorem, Beniere-Hector theorem Aranson-Zhuzhoma's example. 12 Triptych: Geodesic frameworks revisited On continuity and collapse of geodesic frameworks Cr-Closing lemma." @default.
• W285127579 created "2016-06-24" @default.
• W285127579 creator A5030662408 @default.
• W285127579 creator A5034610016 @default.
• W285127579 date "1999-07-15" @default.
• W285127579 modified "2023-10-01" @default.
• W285127579 title "Flows on 2-dimensional Manifolds: An Overview" @default.
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