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Extended Abstracts Spring 2016 pp 141–145Cite as

Birkhäuser

An Equivalent Formulation of the Averaged Functions via Bell Polynomials

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Part of the book series: Trends in Mathematics ((RPCRMB,volume 8))

Abstract

We use Bell polynomials to provide an alternative formula for the averaged functions. This new formula can make the computational implementation of the averaged functions easier.

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References

  1. F. Brouwder, Fixed point theory and nonlinear problems. Bull. Amer. Math. Soc. 9, 1–39 (1983)

    Article  MathSciNet  Google Scholar 

  2. J. Itikawa, J. Llibre, D.D. Novaes, A new result on averaging theory for a classe of discontinuous planar differential systems with applications. Revista Matemática Iberoamericana (2016, to appear)

    Google Scholar 

  3. W.P. Johnson, The curious history of Faá di Bruno’s formula. The Am. Math. Monthly 109(3), 217–234 (2002)

    Article  MATH  Google Scholar 

  4. J. Llibre, D.D. Novaes, On the continuation of periodic solutions in discontinuous dynamical systems (2015). Preprint, arXiv:1504.03008

  5. J. Llibre, R. Moeckel, C. Simó, Central Configurations, Periodic Orbits, and Hamiltonian Systems. Advanced Courses in Mathematics-CRM Barcelona (Birkhäuser, Basel, 2015)

    Google Scholar 

  6. J. Llibre, D.D. Novaes, M.A. Teixeira, Higher order averaging theory for finding periodic solutions via Brouwer degree. Nonlinearity 27, 563–583 (2014)

    Google Scholar 

  7. J. Llibre, D.D. Novaes, M.A. Teixeira, Corrigendum: higher order averaging theory for finding periodic solutions via Brouwer degree. Nonlinearity 27, 2417 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Llibre, A.C. Mereu, D.D. Novaes, Averaging theory for discontinuous piecewise differential systems. J. Differ. Equ. 258, 4007–4032 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Llibre, D.D. Novaes, M.A. Teixeira, On the birth of limit cycles for non-smooth dynamical systems. Bull. Sci. Math. 139, 229–244 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author would like to thank the referees for their helpful comments and suggestions. He is supported by the FAPESP grants 2015/02517-6 and 2015/24841-0 and by the European Community grants FP7-PEOPLE-2012-IRSES-316338 and FP7-PEOPLE-2012-IRSES-318999.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Baruque de Holanda, 651, Cidade Universitária Zeferino Vaz, Campinas, São Paulo, 13083–859, Brazil

    Douglas D. Novaes

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  1. Douglas D. Novaes
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Corresponding author

Correspondence to Douglas D. Novaes .

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Editors and Affiliations

  1. DEIB, Politecnico di Milano , Milano, Italy

    Alessandro Colombo

  2. Department of Engineering Mathematics, University of Bristol , BRISTOL, Avon, United Kingdom

    Mike Jeffrey

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya , Barcelona, Spain

    J. Tomàs Lázaro

  4. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep M. Olm

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Novaes, D.D. (2017). An Equivalent Formulation of the Averaged Functions via Bell Polynomials. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_25

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