Results 31 to 40 of about 274,225 (273)

Polynomial first integrals of quadratic vector fields

Journal of Differential Equations, 2006
The goal of this paper is to characterize those quadratic differential equations in the plane having a polynomial first integral, and to provide an explicit expression of these systems as well as of their polynomial first integrals. It is well known that if the system writes as \[ \dot x=P(x,y), \quad \dot y=Q(x,y) \] it is not restrictive to assume ...
Chavarriga, Javier, García, Belén, Llibre, Jaume, del Río, Jesús S. Pérez, Rodríguez, José Angel   +4 more
openaire   +2 more sources

Quadratic Morse-Smale Vector Fields which are not Structurally Stable [PDF]

Proceedings of the American Mathematical Society, 1982
An example is given of a quadratic system in the plane which is Morse-Smale but not structurally stable. Also, it is proved that no such example exists for a quadratic system which is a gradient.
Chicone, Carmen, Shafer, Douglas S.
openaire   +1 more source

A construction of a large family of commuting pairs of integrable symplectic birational 4-dimensional maps

, 2016
We give a construction of completely integrable 4-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme,
Petrera, Matteo, Suris, Yuri B.
core   +2 more sources

Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading

Advanced Engineering Materials, EarlyView.
The approach by Amor and the approach by Miehe and Zhang for asymmetric damage behavior in the phase field method for fracture are compared regarding their fitness for microcrack‐based failure modeling. The comparison is performed for the case of a dual‐phase microstructure with a brittle and a ductile constituent.
Jakob Huber, Jan Torgersen, Ewald Werner
wiley   +1 more source

Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this article we obtain the geometric classification of singularities, finite and infinite, for the two subclasses of quadratic differential systems with total finite multiplicity $m_f=4$ possessing exactly three finite singularities, namely: systems ...
Joan Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe   +3 more
doaj   +1 more source

Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields [PDF]

, 2007
We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces on two ...
Iosevich, Alex, Koh, Doowon
core  

On integrability of Hirota-Kimura type discretizations

, 2011
We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields.
A. Clebsch, A.G. Reyman, A.M. Perelomov, A.P. Veselov, Andreas Pfadler, F. Golse, F. Musso, G. Kirchhoff, G. R. W. Quispel, G. Suslov, I. Basak, J. Marsden, J.M. Sanz-Serna, K. Kimura, M. Adler, M. Alber, M. Gaudin, M. Petrera, M. Petrera, Matteo Petrera, N. J. Hitchin, R. Hirota, V. Dragović, V. Volterra, W. Kahan, W. Kahan, Yu. B. Suris, Yu. B. Suris, Yuri B. Suris   +28 more
core   +1 more source

Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

International Journal of Bifurcation and Chaos, 2022
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line [Formula: see text], where these kinds of systems have a nilpotent center at [Formula: see text], which comes from the combination of two cusps of both Hamiltonian systems.
Chen, Ting, Llibre, Jaume
openaire   +2 more sources

Predicting Atomic Charges in MOFs by Topological Charge Equilibration

Advanced Functional Materials, EarlyView.
An atomic charge prediction method is presented that is able to accurately reproduce ab‐initio‐derived reference charges for a large number of metal–organic frameworks. Based on a topological charge equilibration scheme, static charges that fulfill overall neutrality are quickly generated.
Babak Farhadi Jahromi, Sumukh Shankar Sharadaprasad, Rochus Schmid   +2 more
wiley   +1 more source

Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this article we obtain the geometric classification of singularities, finite and infinite, for the three subclasses of quadratic differential systems with $m_f=4$ possessing exactly two finite singularities, namely: (i) systems with two double complex
Joan Artés, Jaume Llibre, Alex Rezende, Dana Schlomiuk, Nicolae Vulpe   +4 more
doaj   +1 more source