Isabel S. Labouriau, Adrian C. Murza
Abstract:
We analyze the dynamics of a class of
-equivariant differential
equations of the form
,
where z is complex, the time t is real, while p and s
are complex parameters. This study is the generalisation to
of previous works with
and
symmetry.
We reduce the problem of finding limit cycles to an Abel equation, and
provide criteria for proving in some cases uniqueness and hyperbolicity of
the limit cycle that surrounds either 1, 2n+1 or 4n+1 equilibria,
the origin being always one of these points.
Submitted October 10, 2015. Published May 16, 2016.
Math Subject Classifications: 34C07, 34C14, 34C23, 37C27
Key Words: Planar autonomous ordinary differential equations; limit cycles;
symmetric polynomial systems.
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Isabel S. Labouriau Centro de Matemática da Universidade do Porto Rua do Campo Alegre 687 4169-007 Porto, Portugal email: islabour@fc.up.pt | |
Adrian C. Murza Centro de Matemática da Universidade do Porto Rua do Campo Alegre 687 4169-007 Porto, Portugal email: adrian_murza@hotmail.com |
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