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International Journal of Algebra and Computation, ISSN 0218-1967, 05/2019, Volume 29, Issue 3, pp. 481 - 505
We construct linear bases of free Gelfand–Dorfman–Novikov (GDN) superalgebras. As applications, we prove a Poincaré–Birkhoff–Witt (PBW) type theorem, that is,... 
GDN superalgebra | Poincaré-Birkhoff-Witt theorem | nilpotency
Journal Article
Journal of Algebra, ISSN 0021-8693, 04/2018, Volume 500, pp. 153 - 170
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 6801 - 6822
Journal Article
Journal of Lie Theory, ISSN 0949-5932, 2018, Volume 28, Issue 3, pp. 735 - 756
Hom-type algebras, in particular Hom-Lie algebras, have attracted quite much attention in recent years. A Hom-Lie algebra is called involutive if its Hom map... 
Hom-Lie algebra | Involution | Poincaré-Birkhoff-Witt theorem | Universal enveloping algebra | Hom-associative algebra | MATHEMATICS | Poincare-Birkhoff-Witt theorem | DEFORMATIONS | universal enveloping algebra | involution
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 2150 - 2162
By the use of a higher dimensional version of the Poincaré–Birkhoff theorem, we are able to generalize a result of Jacobowitz and Hartman , thus proving the... 
Superlinear systems | Periodic solutions | Poincaré–Birkhoff theorem | Poincaré-Birkhoff theorem | EXISTENCE | MATHEMATICS | THEOREM | HAMILTONIAN-SYSTEMS | DIFFERENTIAL-EQUATION | Poincare-Birkhoff theorem
Journal Article
Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 6/2013, Volume 13, Issue 2, pp. 611 - 625
We represent several results on the existence of fixed points of the arbitrary topological annulus maps. The celebrated boundary twist condition of the... 
continuous map | Mathematical Methods in Physics | Poincaré–Birkhoff theorem | Secondary 37E40 | fixed point | Analysis | Mathematics, general | Mathematics | Primary 54H25 | Poincaré-Birkhoff theorem | MATHEMATICS | MATHEMATICS, APPLIED | PROOF | Poincare-Birkhoff theorem
Journal Article
São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2018, Volume 12, Issue 2, pp. 246 - 251
We use that the n-sphere for $$n\ge 2$$ n≥2 is simply-connected to prove the Poincaré-Birkhoff-Witt Theorem. 
Mathematics, general | Mathematics | Universal enveloping algebra | Symmetric group | 16S30 | Poincaré-Birkhoff-Witt
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2012, Volume 13, Issue 3, pp. 1292 - 1305
Journal Article
Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 06/2017, Volume 19, Issue 2, pp. 1283 - 1294
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s11784-016-0313-0 In this... 
Exact symplectic map | Poincaré–Birkhoff theorem | Boundary twist condition
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 12, pp. 4166 - 4185
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2015, Volume 258, Issue 9, pp. 3088 - 3106
A geometric method is introduced to study superlinear second order differential equations with impulsive effects. Basing on a reference continuous polar... 
Impulsive differential equation | Partial twist fixed point theorem | Poincaré–Birkhoff theorem | Periodic solutions | Poincaré-Birkhoff theorem | MATHEMATICS | DUFFING EQUATIONS | MULTIPLICITY | HAMILTONIAN-SYSTEMS | BOUNDARY-VALUE-PROBLEMS | Poincare-Birkhoff theorem | 1ST-ORDER | Differential equations
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2019, Volume 473, Issue 1, pp. 490 - 509
Journal Article
Topological Methods in Nonlinear Analysis, ISSN 1230-3429, 2012, Volume 40, Issue 1, pp. 29 - 52
We prove the existence of periodic solutions for a planar non-autonomous Hamiltonian system which is a small perturbation of an autonomous system, in the... 
Nonlinear dynamics | Periodic solutions | Poincaré-birkhoff | DUFFING EQUATIONS | SUBHARMONIC SOLUTIONS | 2ND-ORDER DIFFERENTIAL-EQUATIONS | PROOF | FIXED-POINT THEOREM | MATHEMATICS | Poincare-Birkhoff | GEOMETRIC THEOREM | TRANSLATION THEOREM | RESONANCE | ROTATION NUMBERS | OSCILLATIONS | nonlinear dynamics
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 11/2016, Volume 5, Issue 4, pp. 367 - 382
We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff... 
Poincaré–Birkhoff theorem | 34C25 | perturbation theory | Periodic solutions | 47H15 | Poincaré-Birkhoff theorem | MATHEMATICS | MATHEMATICS, APPLIED | TORI | LEWIS-TYPE THEOREM | KAM | EQUATIONS | ORBITS | Poincare-Birkhoff theorem
Journal Article
Canadian Journal of Mathematics, ISSN 0008-414X, 2013, Volume 65, Issue 2, pp. 241 - 265
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 2007, Volume 42, Issue 11, pp. 1052 - 1065
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 09/2019, Volume 129, pp. 131 - 152
We present a higher-dimensional version of the Poincaré–Birkhoff theorem which applies to Poincaré time maps of Hamiltonian systems. The maps under... 
Hamiltonian systems | Periodic solutions | Poincaré–Birkhoff | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | Poincare-Birkhoff | RELATIVE CATEGORY | SYSTEMS | PROOF | FIXED-POINT THEOREM
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 05/2017, Volume 34, Issue 3, pp. 679 - 698
We propose an extension to higher dimensions of the Poincaré–Birkhoff Theorem which applies to Poincaré time-maps of Hamiltonian systems. Examples of... 
Hamiltonian systems | Periodic solutions | Poincaré–Birkhoff | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | Poincare-Birkhoff | GEOMETRIC THEOREM | MULTIPLICITY | EQUATIONS | SYSTEMS | PROOF | FIXED-POINT THEOREM | FUNCTIONALS
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 08/2018, Volume 38, Issue 8, pp. 3955 - 3975
In [7] the author proved the existence of multiple periodic linear motions with collisions for a periodically forced Kepler problem. We extend this result... 
Poincaré-Birkhoff theorem | Multiple collisions | Periodic solution | periodic solution | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Birkhoff theorem
Journal Article
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