ON THE INTEGRABILITY OF THE DIFFERENTIAL SYSTEMS IN DIMENSION TWO AND OF THE POLYNOMIAL DIFFERENTIAL SYSTEMS IN ARBITRARY DIMENSION

Jaume Llibre

doi:10.11948/2011004

2011 Volume 1 Issue 1

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Jaume Llibre. ON THE INTEGRABILITY OF THE DIFFERENTIAL SYSTEMS IN DIMENSION TWO AND OF THE POLYNOMIAL DIFFERENTIAL SYSTEMS IN ARBITRARY DIMENSION[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 33-52. doi: 10.11948/2011004

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Jaume Llibre. ON THE INTEGRABILITY OF THE DIFFERENTIAL SYSTEMS IN DIMENSION TWO AND OF THE POLYNOMIAL DIFFERENTIAL SYSTEMS IN ARBITRARY DIMENSION[J]. Journal of Applied Analysis & Computation, 2011, 1(1): 33-52. doi: 10.11948/2011004

ON THE INTEGRABILITY OF THE DIFFERENTIAL SYSTEMS IN DIMENSION TWO AND OF THE POLYNOMIAL DIFFERENTIAL SYSTEMS IN ARBITRARY DIMENSION

Jaume Llibre

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

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Abstract

Abstract

This is a survey on recent results providing su-cient conditions for the existence of a flrst integral, flrst for vector flelds deflned on real surfaces, and second for polynomial vector flelds in Rⁿ or Cⁿ with n ≥ 2. We also provide an open question and some applications based on the existence of such flrst integrals.
- First integral /
- 2-dimensional flows /
- Darboux theory of integrability /
- invariant algebraic surface /
- exponential factor
MSC: 34C05;34C14;34C40;37C10;34A34

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References

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