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Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line
Authors: Jaume Llibre
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Abstract
This paper is a survey on the study of the maximum number of limit cycles of planar continuous and discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line L. We restrict our attention to the crossing limit cycles, i.e. to the limit cycles having exactly two points on the straight line L. We summarize the results known by now and describe the tools for obtaining them.Departament de Matem` atiques,
Universitat Aut` onoma de Barcelona,
08193 Bellaterra, Barcelona,
Catalonia, Spain
E-mail:
Universitat Aut` onoma de Barcelona,
08193 Bellaterra, Barcelona,
Catalonia, Spain
E-mail:
Fulltext
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Contents
- Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line
- The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five
- The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
- Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations
- The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3,3)
- On the upper bound of the number of functionally independent focal quantities of the Lyapunov differential system
- On limit cycles of polynomial systems of the first-order ODEs
- Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems.
- Invariant conditions of stability of unperturbed motion governed by critical differential systems s(1,2,3)
- Working with professor Nicolae Vulpe
