Invariant Algebraic Surfaces of Polynomial Vector Fields in Dimension Three
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DOI: 10.1007/s10884-021-10080-8
Abstract: We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension two to dimension three. Such surfaces are… read more here.
Keywords: vector; algebraic surfaces; polynomial vector; dimension three ... See more keywords
Limit cycles of discontinuous piecewise polynomial vector fields
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.11.048
Abstract: Abstract When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x ˙ = − y ( (… read more here.
Keywords: piecewise polynomial; polynomial vector; limit cycles; vector fields ... See more keywords
On the number of Waring decompositions for a generic polynomial vector
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2017.05.016
Abstract: Abstract We prove that a general polynomial vector ( f 1 , f 2 , f 3 ) in three homogeneous variables of degrees ( 3 , 3 , 4 ) has a unique Waring… read more here.
Keywords: vector; polynomial vector; waring decompositions; decompositions generic ... See more keywords
Local cyclicity in low degree planar piecewise polynomial vector fields
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DOI: 10.1016/j.nonrwa.2020.103278
Abstract: Abstract In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles… read more here.
Keywords: piecewise polynomial; polynomial vector; planar piecewise; vector fields ... See more keywords