Results 101 to 110 of about 4,250,304 (141)

Holomorphic foliations with Liouvillian first integrals

Ergodic Theory and Dynamical Systems, 2001
Summary: Intuitively, a Liouvillian function on \(\mathbb{C} P(n)\) is one which is obtained from rational functions by a finite process of integrations, exponentiations and algebraic operations. This paper is devoted to the study of foliations determined by polynomial 1-forms which have a Liouvillian first integral.
Camacho, C., Azevedo Scárdua, B.
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Formal Weierstrass integrability for a Liénard differential system

Journal of Mathematical Analysis and Applications, 2021
A novel algebraic method to verify if a polynomial differential system in C 2 is formal Weierstrass integrable was introduced in [18] , [19] . Here we apply these results to a Lienard differential system finding non-Liouvillian integrable systems.
Brigita Ferčec, J. Giné
semanticscholar   +1 more source

Liouvillian first integrals of differential equations

Banach Center Publications, 2011
In this paper we generalize to any dimension and codimension some theorems about existence of Liouvillian solutions or first integrals proved by M. Singer in Liouvillian first integrals of differential equations (1992) for first order differential equations.
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The Extended Monodromy Group and Liouvillian First Integrals

Journal of Dynamical and Control Systems, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integration of Liouvillian functions with special functions

Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86, 1986
In this paper, we discuss a decision procedure for the indefinite integration of transcendental Liouvillian functions in terms of elementary functions and logarithmic integrals. We also discuss a decision procedure for the integration of a large class of transcendental Liouvillian functions in terms of elementary functions and error-functions.
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Liouvillian Integrability and the Poincaré Problem for Nonlinear Oscillators with Quadratic Damping and Polynomial Forces

Journal of dynamical and control systems, 2020
M. Demina, N. S. Kuznetsov
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Liouvillian first integrals for the planar Lotka-Volterra system

Rendiconti del Circolo Matematico di Palermo, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giacomini, Hector, Cairó, Laurent, Llibre, Jaume   +2 more
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Existence of Liouvillian solutions in the problem of motion of a heavy rigid body with a fixed point under the action of gyroscopic forces in the Hess case

Прикладная математика и механика / Journal of Applied Mathematics and Mechanics
The paper studies the problem of motion of a rigid body about a fixed point under the action of gravity and gyroscopic forces in the Hess integrability case.
A. S. Kuleshov
semanticscholar   +1 more source

Liouvillian integration of the Lotka-Volterra system

Qualitative Theory of Dynamical Systems, 2001
The system of differential equations under consideration is \[ x' = x(Cy+z),\quad y' = y(Az+x),\quad z' = z(Bx+y), \] where \(A\), \(B\), and \(C\) are nonzero complex constants. This system is of broad interest because it typically serves as a normal form for ``factored quadratic systems,'' quadratic homogeneous systems such that \(\alpha\) factors ...
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Complete Reduction for Derivatives in a Transcendental Liouvillian Extension

arXiv.org
Transcendental Liouvillian extensions are differential fields, in which one can model poly-logarithmic, hyperexponential, and trigonometric functions, logarithmic integrals, and their (nested) rational expressions. For such an extension $(F, \, ^\prime)$
Shaoshi Chen, Hao Du, Yiman Gao, Hui Huang, Wenqiao Li, Ziming Li   +5 more
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