A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems |
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Authors: | Jaume Llibre Xiang Zhang |
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Abstract: | In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in and of the discontinuous piecewise differential systems in formed by two linear differential systems separated by a straight line. For this class of discontinuous piecewise differential systems the study of their algebraic and explicit non-algebraic limit cycles just is starting. Here we provide the first explicit non-algebraic limit cycle for the discontinuous piecewise linear differential systems. Additionally we recall seven open questions related with these types of limit cycles. |
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Keywords: | Algebraic limit cycle Non-algebraic limit cycle Explicit limit cycle Polynomial differential system Piecewise linear differential system |
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