Downloads provided by UsageCountsGeometric tools to determine the hyperbolicity of limit cycles
Copyright policy ) Guillamon Grabolosa, Antoni; Sabatini, Marco;
Geometric tools to determine the hyperbolicity of limit cycles
In this paper we present a new method to study limit cycles’ hyperbolicity. The main tool is the function ? = ([V,W] ^ V )/(V ^W), where V is the vector field under investigation and W a transversal one. Our approach gives a high degree of freedom for choosing operators to study the stability. It is related to the divergence test, but provides more information on the system’s dynamics. We extend some previous results on hyperbolicity and apply our results to get limit cycles’ uniqueness. Li´enard systems and conservative+dissipative systems are considered among the applications.
Spain, Spain, Italy
Differential equations, Hyperbolicity, hyperbolicity, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], limit cycles, Lie brackets, Applied Mathematics, Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Stability of solutions to ordinary differential equations, Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Limit cycles, Structural stability and analogous concepts of solutions to ordinary differential equations, hyperbolicity of limit cycles, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], :34 Ordinary differential equations::34A General theory [Classificació AMS], Differentiable dynamical systems, Hyperbolicity; limit cycle; uniqueness; divergence; Lie brackets; Lienard equation, Equacions diferencials ordinàries, Classificació AMS::34 Ordinary differential equations::34A General theory, Liénard systems, Cicles límits, Analysis
Differential equations, Hyperbolicity, hyperbolicity, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], limit cycles, Lie brackets, Applied Mathematics, Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Stability of solutions to ordinary differential equations, Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Limit cycles, Structural stability and analogous concepts of solutions to ordinary differential equations, hyperbolicity of limit cycles, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], :34 Ordinary differential equations::34A General theory [Classificació AMS], Differentiable dynamical systems, Hyperbolicity; limit cycle; uniqueness; divergence; Lie brackets; Lienard equation, Equacions diferencials ordinàries, Classificació AMS::34 Ordinary differential equations::34A General theory, Liénard systems, Cicles límits, Analysis
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