The Existential Hilbert 16th problem and an estimate for cyclicity of elementary polycycles

  title={The Existential Hilbert 16th problem and an estimate for cyclicity of elementary polycycles},
  author={Vadim Kaloshin},
The Existential Hilbert Problem is a weak version of the part b of the Hilbert 16-th problem which also asks not only about the number, but also about position of limit cycles of (1). The problem about finiteness of number of limit cycles for an individual polynomial line field (1) is called Dulac problem, since the pioneering work of Dulac [Du], who claimed in 1923 to solve this problem, but an error was found. The Dulac problem was solved by two independent and rather different proofs given… CONTINUE READING
Highly Cited
This paper has 18 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 42 references

Centennial history of the Hilbert 16th problem

  • Ilyashenko, Yu
  • Bull. Am. Math. Soc
  • 2002

Hilbert-Arnold Problem and an estimate for cyclicity of polycycles on the plane and in the space

  • V. Kaloshin
  • Funct. Anal. Appl
  • 2001

Normal forms near a saddle-node and applications to finite cyclicity of graphics

  • F. DIR Dumortier, Ilyashenko, Yu, C. Rousseau
  • 2000

Bifurcations of planar and spatial polycycles: Arnold’s program and its development

  • IK Ilyashenko, Yu, V. Kaloshin
  • Fields Inst. Commun
  • 1999

Bifurcation of planar vector fields and Hilbert’s sixteenth problem

  • R. Roussarie
  • Progr. Math. 164. Birkhäuser Verlag, Basel
  • 1998

Bifurcations of polycycles an “apple” and a “half-apple” in generic two-parameter families (in Russian)

  • T. Grozovskii
  • Differ. Equations
  • 1996

Cyclicity of elementary polycycles in generic smooth vector fields, Differential equations with real and complex time, Yu

  • S. Trifonov
  • Ilyashenko (ed.). Proc. Steklov Inst. Math. 213,
  • 1996

Few-Parameter Generic Families on the Sphere

  • A. KS Kotova, V. Stanzo
  • Am. Math. Soc. Transl.,
  • 1996

Similar Papers

Loading similar papers…