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

Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 2, pp. 1064 - 1084

We provide a geometric assumption which unifies and generalizes the conditions proposed in , so to obtain a higher dimensional version of the Poincaré–Birkhoff...

Hamiltonian systems | Poincaré–Birkhoff Theorem | Avoiding cones condition | Periodic solutions | MATHEMATICS | PERIODIC-SOLUTIONS | CRITICAL-POINT THEORY | Poincare-Birkhoff Theorem | HAMILTONIAN-SYSTEMS | RELATIVE CATEGORY | STRONGLY INDEFINITE FUNCTIONALS

Hamiltonian systems | Poincaré–Birkhoff Theorem | Avoiding cones condition | Periodic solutions | MATHEMATICS | PERIODIC-SOLUTIONS | CRITICAL-POINT THEORY | Poincare-Birkhoff Theorem | HAMILTONIAN-SYSTEMS | RELATIVE CATEGORY | STRONGLY INDEFINITE FUNCTIONALS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2014, Volume 366, Issue 11, pp. 5903 - 5923

Through the method of brick decomposition and the operations on essential topological lines, we generalize the line translation theorem of Beguin, Crovisier...

MATHEMATICS | PSEUDO-ROTATIONS | POINCARE-BIRKHOFF THEOREM | OPEN ANNULUS

MATHEMATICS | PSEUDO-ROTATIONS | POINCARE-BIRKHOFF THEOREM | OPEN ANNULUS

Journal Article

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, ISSN 1661-7738, 06/2017, Volume 19, Issue 2, pp. 1283 - 1294

In this paper, using a generalized version of the Poincar,-Birkhoff theorem due to Franks, we prove the existence of at least two geometrically distinct...

MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRIC THEOREM | MULTIPLICITY | Exact symplectic map | HAMILTONIAN-SYSTEMS | PENDULUM | PLANE | Boundary twist condition | Poincare-Birkhoff theorem

MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRIC THEOREM | MULTIPLICITY | Exact symplectic map | HAMILTONIAN-SYSTEMS | PENDULUM | PLANE | Boundary twist condition | Poincare-Birkhoff theorem

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 1, pp. 349 - 370

In this paper we are concerned with the existence of periodic solutions for semilinear Duffing equations with impulsive effects. Firstly for its autonomous...

Periodic solutions | Impulsive differential equations | Poincaré–Birkhoff twist theorem | MATHEMATICS | MATHEMATICS, APPLIED | RESONANCE | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | SYSTEMS | Poincare-Birkhoff twist theorem | POINCARE-BIRKHOFF THEOREM

Periodic solutions | Impulsive differential equations | Poincaré–Birkhoff twist theorem | MATHEMATICS | MATHEMATICS, APPLIED | RESONANCE | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | SYSTEMS | Poincare-Birkhoff twist theorem | POINCARE-BIRKHOFF THEOREM

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

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 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

11.
Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras

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

12.
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

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2011, Volume 5, Issue 1, pp. 147 - 158

In this paper we establish three different existence results for periodic solutions for a class of first-order neutral differential equations. The first one is...

Integers | Mathematical theorems | Homeomorphism | Differential equations | Diagonal lemma | Sine function | Differentials | Spherical coordinates | Continuous functions | First-order neutral differential equations | Krasnoselskii fixed point theorem | Infinite periodic solutions | Mawhin's continuation theorem | Generalized Poincare-Birkhoff fixed point theorem | first-order neutral differential equations | MATHEMATICS | MATHEMATICS, APPLIED | PROOF | DELAY EQUATIONS | generalized Poincare-Birkhoff fixed point theorem | POINCARE-BIRKHOFF THEOREM

Integers | Mathematical theorems | Homeomorphism | Differential equations | Diagonal lemma | Sine function | Differentials | Spherical coordinates | Continuous functions | First-order neutral differential equations | Krasnoselskii fixed point theorem | Infinite periodic solutions | Mawhin's continuation theorem | Generalized Poincare-Birkhoff fixed point theorem | first-order neutral differential equations | MATHEMATICS | MATHEMATICS, APPLIED | PROOF | DELAY EQUATIONS | generalized Poincare-Birkhoff fixed point theorem | POINCARE-BIRKHOFF THEOREM

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

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

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 11/2016, Volume 38, Issue 4, pp. 1 - 20

In reversible dynamical systems, it is of great importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of...

DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISMS | GEOMETRIC THEOREM | PLANE | DYNAMICS | ORBITS | PROOF | FLOWS | POINCARE-BIRKHOFF THEOREM | SURFACES | Annuli | Dynamical systems | Maps

DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISMS | GEOMETRIC THEOREM | PLANE | DYNAMICS | ORBITS | PROOF | FLOWS | POINCARE-BIRKHOFF THEOREM | SURFACES | Annuli | Dynamical systems | Maps

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

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 03/2017, Volume 37, Issue 3, pp. 1425 - 1436

We consider a nonautonomous Hamiltonian system, T-periodic in time, possibly defined on a bounded space region, the boundary of which consists of singularity...

Poincarë-Birkhö theorem | Hamiltonian systems | Rotation number | Singularities | Periodic solutions | MATHEMATICS | MATHEMATICS, APPLIED | singularities | rotation number | EQUATIONS | Poincare-Birkhoff theorem

Poincarë-Birkhö theorem | Hamiltonian systems | Rotation number | Singularities | Periodic solutions | MATHEMATICS | MATHEMATICS, APPLIED | singularities | rotation number | EQUATIONS | Poincare-Birkhoff theorem

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 72, Issue 11, pp. 4005 - 4015

We prove multiplicity of periodic solutions for a scalar second order differential equation with an asymmetric nonlinearity, thus generalizing previous results...

Nonlinear boundary value problems | Multiplicity of periodic solutions | Poincaré–Birkhoff Theorem | Poincaré-Birkhoff Theorem | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Birkhoff Theorem | Scalars | Nonlinearity | Theorems | Asymmetry | Proving | Differential equations

Nonlinear boundary value problems | Multiplicity of periodic solutions | Poincaré–Birkhoff Theorem | Poincaré-Birkhoff Theorem | MATHEMATICS | MATHEMATICS, APPLIED | Poincare-Birkhoff Theorem | Scalars | Nonlinearity | Theorems | Asymmetry | Proving | Differential equations

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

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