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

GDN superalgebra | Poincaré-Birkhoff-Witt theorem | nilpotency

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2018, Volume 500, pp. 153 - 170

In 1997, X. Xu invented a concept of Novikov–Poisson algebras (we call them Gelfand–Dorfman–Novikov–Poisson (GDN–Poisson) algebras). We construct a linear...

GDN–Poisson algebra | Special GDN–Poisson admissible algebra | Poincaré–Birkhoff–Witt theorem | GDN-Poisson algebra | Special GDN-Poisson admissible algebra | Poincaré-Birkhoff-Witt theorem | DERIVATION | BRACKETS | CHARACTERISTIC-0 | algebra | NONASSOCIATIVE-ALGEBRAS | Special GDN-Poisson admissible | LIE-ALGEBRAS | MATHEMATICS | Poincare-Birkhoff-Witt theorem | MODULES | HAMILTONIAN OPERATORS | SUPERALGEBRAS | HYDRODYNAMIC TYPE | Mathematics - Rings and Algebras

GDN–Poisson algebra | Special GDN–Poisson admissible algebra | Poincaré–Birkhoff–Witt theorem | GDN-Poisson algebra | Special GDN-Poisson admissible algebra | Poincaré-Birkhoff-Witt theorem | DERIVATION | BRACKETS | CHARACTERISTIC-0 | algebra | NONASSOCIATIVE-ALGEBRAS | Special GDN-Poisson admissible | LIE-ALGEBRAS | MATHEMATICS | Poincare-Birkhoff-Witt theorem | MODULES | HAMILTONIAN OPERATORS | SUPERALGEBRAS | HYDRODYNAMIC TYPE | Mathematics - Rings and Algebras

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 6801 - 6822

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation (ϕp(x′))′+g(x)=e(t),...

harmonic and subharmonic solutions | superlinear | quasilinear equation | Poincaré‐Birkhoff twist theorem | time map | Quasilinear equation | Time map | Poincaré-Birkhoff twist theorem | Harmonic and subharmonic solutions | Superlinear | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | SINGULARITIES | BOUNDEDNESS | ODE | P-LAPLACIAN | SEMILINEAR DUFFING EQUATIONS | RESONANCE | SYSTEMS | Poincare-Birkhoff twist theorem | Existence theorems | Theorems

harmonic and subharmonic solutions | superlinear | quasilinear equation | Poincaré‐Birkhoff twist theorem | time map | Quasilinear equation | Time map | Poincaré-Birkhoff twist theorem | Harmonic and subharmonic solutions | Superlinear | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | SINGULARITIES | BOUNDEDNESS | ODE | P-LAPLACIAN | SEMILINEAR DUFFING EQUATIONS | RESONANCE | SYSTEMS | Poincare-Birkhoff twist theorem | Existence theorems | Theorems

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

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

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

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

Mathematics, general | Mathematics | Universal enveloping algebra | Symmetric group | 16S30 | Poincaré-Birkhoff-Witt

Journal Article

8.
Full Text
Applications of the Poincaré–Birkhoff theorem to impulsive Duffing equations at resonance

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2012, Volume 13, Issue 3, pp. 1292 - 1305

Many dynamical systems possess an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical...

Periodic solution | Poincaré–Birkhoff theorem | Impulsive Duffing equation | Poincaré-Birkhoff theorem | EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | ASYMMETRIC NONLINEARITIES | SYSTEMS | MODEL | Poincare-Birkhoff theorem | Differential equations | Construction | Theorems | Mathematical analysis | Evolution | Nonlinearity | Duffing equation | Dynamical systems

Periodic solution | Poincaré–Birkhoff theorem | Impulsive Duffing equation | Poincaré-Birkhoff theorem | EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | ASYMMETRIC NONLINEARITIES | SYSTEMS | MODEL | Poincare-Birkhoff theorem | Differential equations | Construction | Theorems | Mathematical analysis | Evolution | Nonlinearity | Duffing equation | Dynamical systems

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

Exact symplectic map | Poincaré–Birkhoff theorem | Boundary twist condition

Journal Article

10.
Universal enveloping algebras and poincaré-birkhoff-witt theorem for involutive hom-lie Algebras

Journal of Lie Theory, ISSN 0949-5932, 2018, Volume 21, Issue 3, pp. 739 - 759

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 12, pp. 4166 - 4185

In the general setting of a planar first order system with , we study the relationships between some classical nonresonance conditions (including the...

Multiple periodic solutions | Poincaré–Birkhoff theorem | Resonance | Rotation number | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | ASYMMETRIC NONLINEARITIES | LANDESMAN-LAZER CONDITIONS | INDEX | Poincare-Birkhoff theorem | ORDINARY DIFFERENTIAL-EQUATIONS | Theorems | Infinity | Mathematical analysis | Images | Nonlinearity | Scalars | Nonresonance | Estimates

Multiple periodic solutions | Poincaré–Birkhoff theorem | Resonance | Rotation number | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | ASYMMETRIC NONLINEARITIES | LANDESMAN-LAZER CONDITIONS | INDEX | Poincare-Birkhoff theorem | ORDINARY DIFFERENTIAL-EQUATIONS | Theorems | Infinity | Mathematical analysis | Images | Nonlinearity | Scalars | Nonresonance | Estimates

Journal Article

12.
Full Text
Periodic solutions of superlinear impulsive differential equations: A geometric approach

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

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

We deal with the -periodic problem associated with a nonlinear scalar differential equation like where, for and , the nonlinearity is assumed behave linearly,...

Poincaré–Birkhoff theorem | Morse index | Landesman–Lazer conditions | Rotation number | Periodic solutions | MATHEMATICS, APPLIED | THEOREM | Landesman-Later conditions | MULTIPLE PERIODIC-SOLUTIONS | LINEAR DUFFING EQUATIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | MATHEMATICS | RESONANCE | SYSTEMS | LANDESMAN-LAZER CONDITIONS | INDEX | Poincare-Birkhoff theorem

Poincaré–Birkhoff theorem | Morse index | Landesman–Lazer conditions | Rotation number | Periodic solutions | MATHEMATICS, APPLIED | THEOREM | Landesman-Later conditions | MULTIPLE PERIODIC-SOLUTIONS | LINEAR DUFFING EQUATIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | MATHEMATICS | RESONANCE | SYSTEMS | LANDESMAN-LAZER CONDITIONS | INDEX | Poincare-Birkhoff theorem

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

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

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

Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange's theorem for Hopf monoids in the category of connected species....

Generating series | Partition | Composition | Poincaré-Birkhoff-Witt theorem | Primitive element | Graded Hopf algebras | Cyclic order | Hopf monoids | Derangement | Lagrange's theorem | Lie kernel | Linear order | Hopf kernel | Species | linear order | FREENESS | generating series | cyclic order | SYM | CROSSED-PRODUCTS | SUBALGEBRAS | TENSOR CATEGORIES | QSYM | MATHEMATICS | ALGEBRAS | Poincare-Birkhoff-Witt theorem | partition | species | composition | graded Hopf algebras | derangement | primitive element

Generating series | Partition | Composition | Poincaré-Birkhoff-Witt theorem | Primitive element | Graded Hopf algebras | Cyclic order | Hopf monoids | Derangement | Lagrange's theorem | Lie kernel | Linear order | Hopf kernel | Species | linear order | FREENESS | generating series | cyclic order | SYM | CROSSED-PRODUCTS | SUBALGEBRAS | TENSOR CATEGORIES | QSYM | MATHEMATICS | ALGEBRAS | Poincare-Birkhoff-Witt theorem | partition | species | composition | graded Hopf algebras | derangement | primitive element

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 2007, Volume 42, Issue 11, pp. 1052 - 1065

We construct the universal enveloping algebra of a Leibniz -algebra and we prove that the category of modules over this algebra is equivalent to the category...

Gröbner bases | Leibniz [formula omitted]-algebra | Universal enveloping algebra | Poincaré–Birkhoff–Witt theorem | Leibniz n-algebra | Poincaré-Birkhoff-Witt theorem | MATHEMATICS, APPLIED | Poincare-Birkhoff-Witt theorem | Grobner bases | COMPUTER SCIENCE, THEORY & METHODS | universal enveloping algebra | NONCOMMUTATIVE GROBNER BASES

Gröbner bases | Leibniz [formula omitted]-algebra | Universal enveloping algebra | Poincaré–Birkhoff–Witt theorem | Leibniz n-algebra | Poincaré-Birkhoff-Witt theorem | MATHEMATICS, APPLIED | Poincare-Birkhoff-Witt theorem | Grobner bases | COMPUTER SCIENCE, THEORY & METHODS | universal enveloping algebra | NONCOMMUTATIVE GROBNER BASES

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

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

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

Poincaré-Birkhoff theorem | Multiple collisions | Periodic solution | periodic solution | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Birkhoff theorem

Journal Article

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