Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Li\'{e}nard's system and Smale's problem   In this paper, using geometric properties of the field rotation parameters,
we present a solution of Smale's Thirteenth Problem on the maximum number of
limit cycles for Li\'{e}nard's polynomial system. We also generalize the
obtained result and present a solution of Hilbert's Sixteenth Problem on the
maximum number of limit cycles surrounding a singular point for an arbitrary
polynomial system. Besides, we consider a generalized Li\'{e}nard's cubic
system with three finite singularities, for which the developed geometric
approach can complete its global qualitative analysis: in particular, it easily
solves the problem on the maximum number of limit cycles in their different
distribution. We give also an alternative proof of the main theorem for the
generalized Li\'{e}nard's system applying the Wintner-Perko termination
principle for multiple limit cycles and discuss some other results concerning
this system.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga