On the periodic solutions of perturbed 4D non-resonant systems. Llibre, J., Novaes, D. D., & Teixeira, M. A. The São Paulo Journal of Mathematical Sciences, 9(2):229-250, December, 2015.
On the periodic solutions of perturbed 4D non-resonant systems [link]Paper  doi  abstract   bibtex   
We provide sufficient conditions for the existence of periodic solutions of a 4D non-resonant system perturbed by smooth or non-smooth functions. We apply these results to study the small amplitude periodic solutions of the non-linear planar double pendulum perturbed by smooth or non-smooth function.
@article{llibre2015periodic,
  abstract = {We provide sufficient conditions for the existence of periodic solutions of a 4D non-resonant system perturbed by smooth or non-smooth functions. We apply these results to study the small amplitude periodic solutions of the non-linear planar double pendulum perturbed by smooth or non-smooth function.},
  added-at = {2015-12-28T06:27:39.000+0100},
  author = {Llibre, J. and Novaes, D. D. and Teixeira, M. A.},
  biburl = {http://www.bibsonomy.org/bibtex/2f7b35b6370c8bd555da0bf340235237a/ddnovaes},
  doi = {10.1007/s40863-015-0017-1},
  interhash = {cc87b68a449a628979f12cf934955218},
  intrahash = {f7b35b6370c8bd555da0bf340235237a},
  journal = {The S{\~{a}}o Paulo Journal of Mathematical Sciences},
  keywords = {myown published},
  month = dec,
  number = 2,
  pages = {229-250},
  timestamp = {2015-12-28T06:27:39.000+0100},
  title = {On the periodic solutions of perturbed 4D non-resonant systems},
  url = {http://link.springer.com/article/10.1007/s40863-015-0017-1},
  volume = 9,
  year = 2015
}

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