The Poincaré-Bendixson theorem: from Poincaré to the XXIst century
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Publication:1935656
DOI10.2478/s11533-012-0110-yzbMath1417.37001OpenAlexW1975878992MaRDI QIDQ1935656
Publication date: 18 February 2013
Published in: Central European Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: http://ruj.uj.edu.pl/xmlui/handle/item/530
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Smooth dynamical systems: general theory (37Cxx) Qualitative theory for ordinary differential equations (34Cxx)
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Cites Work
- A topological characterization of \(\omega\)-limit sets for continuous flows on the projective plane
- Poincaré-Bendixson theorems for meromorphic connections and holomorphic homogeneous vector fields
- Structural stability on two-dimensional manifolds
- The Poincaré-Bendixson theorem on the Klein bottle for continuous vector fields
- A Poincaré-Bendixson theorem for scalar reaction diffusion equations
- Limit sets and the Poincaré-Bendixson theorem in impulsive semidynamical systems
- Cones of rank 2 and the Poincaré-Bendixson property for a new class of monotone systems
- A corollary of the Poincaré-Bendixson theorem and periodic canards
- Orbital stability for ordinary differential equations
- On asymptotically autonomous differential equations in the plane
- Nonlinear differential equations and dynamical systems
- Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
- Poincaré-Bendixson theory for certain retarded functional differential equations
- Counterexamples to the Seifert conjecture and opening closed leaves of foliations
- Existence of periodic orbits on 2-manifolds
- Smoothing continuous flows on 2-manifolds
- A characterization of the \(\omega\)-limit sets of planar continuous dynamical systems
- The Poincaré-Bendixson theorems for two-dimensional semiflows
- One-dimensional chain recurrent sets of flows in the 2-sphere
- A class of flows on 2-manifolds with simple recurrence
- Does distribution theory contain means for extending Poincaré-Bendixson theory?
- A note on the Poincaré-Bendixson index theorem
- Regular families of curves
- A smooth counterexample to the Seifert conjecture
- The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
- Application of the Poincaré-Bendixson theorem
- On dynamical systems in the plane
- Local semi-dynamical systems
- Attraction and nonsaddle sets in dynamical systems
- On the existence of periodic solutions on 2-manifolds
- Poincaré-Bendixson type theorems for two-dimensional manifolds different from the torus
- Sur la dépendance des solutions d'un système d'équations différentielles de leurs seconds membres. Application aux systèmes presque autonomes
- Competitive systems with migration and the Poincaré-Bendixson theorem for a 4-dimensional case
- Continuity in semidynamical systems
- Cohomology of chain recurrent sets
- Flows with cyclic winding numbers groups.
- Existence of periodic orbits of autonomous ordinary differential equations
- Stable closed orbits in plane autonomous dynamical systems.
- The topological structure of solution spaces of ordinary differential equations
- Regular Families of Curves
- A dynamical system on 𝐸⁴ neither isomorphic nor equivalent to a differential system
- The Poincare-Bendixson Theorem for the Klein Bottle
- On the Number of Recurrent Orbit Closures
- A Generalization of a Poincare-Bendixson Theorem to Closed Two-Dimensional Manifolds
- Closed Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations
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