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Meromorphic first integrals of analytic diffeomorphisms
We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound ...
Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3
(PERGAMON-ELSEVIER SCIENCE LTD, 2009)
In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.
Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
(2021-01-01)
Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of ...
On first integrals of the geodesic flow on Heisenberg nilmanifolds
(Elsevier Science, 2016-12)
In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an application we develop the ...
Darboux integrability for polynomial vector fields invariant under action of finite group
(Qualitative Theory of Dynamical Systems, 2018)
The geodesic flow on nilpotent lie groups of steps two and three
(American Institute of Mathematical Sciences, 2021-09)
The goal of this paper is the study of the integrability of the geodesic flow on k-step nilpotent Lie groups, k=2,3, when equipped with a leftinvariant metric. Liouville integrability is proved in low dimensions. Moreover, ...
On the computation of Darboux first integrals of a class of planar polynomial vector fields
We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏i=1 rfi αi, where the αi's are positive real numbers and the fi's are polynomials defining curves with only one place at ...
Darboux–Jouanolou–Ghys integrability for one-dimensional foliations on toric varieties
(Bulletin des Sciences Mathématiques, 2018)
The concept of quasi-integrability: a concrete example
(SPRINGER, 2011)
We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite ...
Integral imprópria e funções Eulerianas
(Universidade Tecnológica Federal do ParanáCampo Mourao, 2010)
This document contains the definitions and classifications of Improper Integrals (first, second and third kind), demonstration of some theorems used to test for convergence and divergence of Improper Integrals (comparison ...