Definitions and examples / 1: |
Preliminaries / 1.1: |
Basic constructions / 1.2: |
The projection method / 1.2.1: |
The universal covering method / 1.2.2: |
The suspension method / 1.2.3: |
Whitney theorem / 1.2.4: |
Connected sum of flows / 1.2.5: |
The branch covering method / 1.2.6: |
Basic examples / 1.3: |
Gradient and Morse-Smale flows / 1.3.1: |
Transitive flows / 1.3.2: |
Flows with Cantor type limit sets / 1.3.3: |
Area preserving and Hamiltonian flows / 1.3.4: |
Harmonic and geodesic vector fields / 1.3.5: |
Poincare-Bendixson's theory / 2: |
Existence of closed transversal / 2.1: |
Absence of non-trivial recurrent trajectories on some surfaces / 2.2: |
Hilmy's and Cherry's theorems on quasiminimal sets / 2.3: |
Maier's theorems on quasiminimal sets / 2.4: |
Gutierrez's structure theorem / 2.5: |
Limit set of individual trajectory / 2.6: |
List of limit and minimal sets / 2.6.1: |
Results of Solntzev and Vinograd / 2.6.2: |
On the existence of minimal sets / 2.6.3: |
Decomposition of flows / 3: |
Decomposition theorems / 3.1: |
Irreducible flows on torus / 3.1.1: |
Canonical neighborhood / 3.1.2: |
Gardiner - Levitt's decomposition / 3.1.3: |
Pants decomposition / 3.1.4: |
Decomposition of area preserving and Hamiltonian flows / 3.1.5: |
Center of flow / 3.2: |
Blowing-down of flows / 3.3: |
Regular flows / 3.4: |
Singular trajectories / 3.4.1: |
Cells / 3.4.2: |
Application: smoothing of flows / 3.5: |
Local theory / 4: |
Topological normal forms / 4.1: |
Analytical normal forms / 4.2: |
Smooth normal forms / 4.3: |
Finitely smooth normal forms / 4.4: |
Degenerate critical points / 4.5: |
C1 normal forms of degenerate singularities / 4.6: |
Space of flows and vector fields / 5: |
Structural stability / 5.1: |
Peixoto's graphs. Classification of Morse-Smale flows / 5.2: |
Rotation systems / 5.2.1: |
Peixoto theorems / 5.2.2: |
Peixoto's counterexample revisited / 5.2.3: |
Lyapunov's method / 5.3: |
Lyapunov functions / 5.3.1: |
Lyapunov graphs / 5.3.2: |
Connected components of Morse-Smale flows / 5.4: |
Degrees of non-stability / 5.5: |
Typical properties of non-stable flows / 5.6: |
Ergodic theory / 6: |
Liouville's theorem / 6.1: |
Kolmogorov's theorem for flows on torus / 6.2: |
Non-trivial invariant measures / 6.3: |
Ergodicity / 6.4: |
Mixing / 6.5: |
Entropy / 6.6: |
Invariants of surface flows / 7: |
Topological classification of torus flows / 7.1: |
Rotation numbers / 7.1.1: |
Classification of minimal flows / 7.1.2: |
Classification of the Denjoy flows / 7.1.3: |
Classification of flows of the Cherry type / 7.1.4: |
Oriented surfaces of genus ≥ 2 / 7.2: |
Aranson-Grines homotopy rotation class / 7.2.1: |
Homotopy rotation orbit / 7.2.2: |
Equivalence of irrational flows / 7.2.3: |
Properties of the homotopy rotation classes / 7.2.4: |
Application of geodesic laminations / 7.3: |
Transitive flows on non-orientable surfaces / 7.4: |
Torus with a cross-cup / 7.4.1: |
Non-orientable surfaces of genus ≥ 4 / 7.4.2: |
Classification of exceptional minimal sets / 7.5: |
Classification of the regular flows / 7.6: |
Leontovich-Maier's theorem for sphere flows / 7.6.1: |
Neumann-O'Brien's orbit complex / 7.6.2: |
Bolsinov-Fomenko's classification of Hamiltonian flows / 7.6.3: |
Classification of non-wandering flows / 7.7: |
Elementary cells of non-wandering flows / 7.7.1: |
Conley-Lyapunov-Peixoto graphs / 7.7.2: |
Equivalence Problem / 7.7.3: |
Realization Problem / 7.7.4: |
Cayley graph of a flow / 7.8: |
Finite groups and Cayley graphs / 7.8.1: |
Isomorphism Problem / 7.8.2: |
Homology and cohomology invariants / 7.8.3: |
Asymptotic cycles / 7.9.1: |
Fundamental class of A. Katok / 7.9.2: |
Zorich's cycles / 7.9.3: |
Rotation sets of surface flows / 7.10: |
Smooth classification of flows / 7.11: |
Torus and Klein bottle / 7.11.1: |
Closed orientable surfaces of genus ≥ 2 / 7.11.2: |
C*-algebras of surface flows / 8: |
Irrational rotation algebra / 8.1: |
Dimension groups / 8.1.1: |
Continued fractions / 8.1.2: |
Effros-Shen's Theorem / 8.1.3: |
Embedding of Aα / 8.1.4: |
Projections of Aα / 8.1.5: |
Morita Equivalence / 8.1.6: |
Artin's rotation algebra / 8.2: |
Myrberg's Approximationssatz / 8.2.1: |
Artin's numbers / 8.2.2: |
K-theory / 8.3: |
Torus with Reeb's components / 8.3.1: |
Baum-Connes Conjecture / 8.3.2: |
C*-algebras of Morse-Smale flows / 8.4: |
Semi-local theory / 9: |
Denjoy's and Schwarz's theorems / 9.1: |
Cherry's problem / 9.2: |
Local structure preventing quasiminimality / 9.3: |
Anosov-Weil problem / 10: |
Theorems of Weil and Anosov / 10.1: |
Asymptotic directions / 10.1.1: |
Weil's theorem and Weil's conjecture / 10.1.2: |
Anosov's theorem / 10.1.3: |
Proof of Weil's conjecture and Weil's theorem / 10.1.4: |
Asymptotic direction of individual curves / 10.2: |
Non-trivial recurrent semi-trajectories / 10.2.1: |
Trajectories of analytic flows / 10.2.2: |
Leaves of foliation / 10.2.3: |
Curves with restriction on the geodesic curvature / 10.2.4: |
Approximation of curve by trajectories of a flow / 10.3: |
Limit sets of curves and trajectories at the absolute / 10.4: |
Deviation of curves from the geodesies / 10.5: |
The deviation property of trajectories / 10.5.1: |
Deviation from the geodesic frameworks / 10.5.2: |
Branched coverings / 10.5.3: |
Swing of trajectories near hyperbolic lines / 10.5.4: |
Examples of unbounded deviation / 10.6: |
Surfaces of genus ≥ 2 / 10.6.1: |
Irrational direction on torus / 10.6.2: |
Rational direction on torus / 10.6.3: |
Non-compact surfaces / 11: |
Kaplan's classification / 11.1: |
Level curves of harmonic functions / 11.2: |
Markus's classification / 11.3: |
Neumann's example / 11.4: |
Inaba's example and Beniere-Meigniez's theorem / 11.6: |
Beniere-Hector's theorem / 11.7: |
Aranson-Zhuzhoma's example / 11.8: |
Triptych / 12: |
Geodesic frameworks revisited / 12.1: |
On continuity and collapse of geodesic frameworks / 12.2: |
Cr-closing lemma / 12.3: |
Definitions and examples / 1: |
Preliminaries / 1.1: |
Basic constructions / 1.2: |