@article {FONDA20171064,
	title = {An avoiding cones condition for the Poincar{\'e}{\textendash}Birkhoff Theorem},
	journal = {Journal of Differential Equations},
	volume = {262},
	number = {2},
	year = {2017},
	pages = {1064 - 1084},
	abstract = {<p>We provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point Theorem for Poincar{\'e} maps of Hamiltonian systems.</p>},
	keywords = {Avoiding cones condition, Hamiltonian systems, Periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem},
	issn = {0022-0396},
	doi = {https://doi.org/10.1016/j.jde.2016.10.002},
	url = {http://www.sciencedirect.com/science/article/pii/S0022039616303278},
	author = {Alessandro Fonda and Paolo Gidoni}
}
@article {BOSCAGGIN20114166,
	title = {Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincar{\'e}{\textendash}Birkhoff theorem},
	journal = {Nonlinear Analysis: Theory, Methods \& Applications},
	volume = {74},
	number = {12},
	year = {2011},
	pages = {4166 - 4185},
	abstract = {<p>In the general setting of a planar first order system (0.1)u'=G(t,u),u∈R2, with G:[0,T]{\texttimes}R2{\textrightarrow}R2, we study the relationships between some classical nonresonance conditions (including the Landesman{\textendash}Lazer one) {\textemdash} at infinity and, in the unforced case, i.e. G(t,0)=0, at zero {\textemdash} and the rotation numbers of {\textquotedblleft}large{\textquotedblright} and {\textquotedblleft}small{\textquotedblright} solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincar{\'e}{\textendash}Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju'=∇uH(t,u) and unforced undamped scalar second order equations x"+g(t,x)=0. In particular, by means of the Landesman{\textendash}Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.</p>},
	keywords = {Multiple periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem, Resonance, Rotation number},
	issn = {0362-546X},
	doi = {https://doi.org/10.1016/j.na.2011.03.051},
	url = {http://www.sciencedirect.com/science/article/pii/S0362546X11001817},
	author = {Alberto Boscaggin and Maurizio Garrione}
}
