Altres ajuts: Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276) In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i.e. in the problem of distinguishing between a focus and a center.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2020.111746&type=result"></script>');
-->
</script>
Green | |
bronze |
citations | 1 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2020.111746&type=result"></script>');
-->
</script>
handle: 10272/23306
The first three authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I +D+I co-financed with FEDER funds, in the frame of the project PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276, P12-FQM-1658, UHU126150 and P20 00764). The last author is partially supported by the Agencia Estatal de Investigación, Spain grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618. For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term. Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2023.113304&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 1 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2023.113304&type=result"></script>');
-->
</script>
handle: 10459.1/65973
In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.jde.2019.01.015&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 13 | |
popularity | Top 10% | |
influence | Average | |
impulse | Top 10% |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.jde.2019.01.015&type=result"></script>');
-->
</script>
handle: 10272/20906 , 10459.1/58355
The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first and second authors are supported by a MINECO/FEDER grant number MTM2010-20907-C02-02 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658; TIC-130 and FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family. Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/s10440-014-0001-2&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 2 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/s10440-014-0001-2&type=result"></script>');
-->
</script>
doi: 10.3934/cpaa.2020021
handle: 10459.1/72915
Recently, in [9] is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. In this work we solve the remaining case completing the analytic integrability problem for such singularity. The first, second and third authors are partially supported by a MINECO/ FEDER grant number MTM2014-56272-C2-2 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276). The fourth author is partially supported by a MINECO/ FEDER grant number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.3934/cpaa.2020021&type=result"></script>');
-->
</script>
Green | |
gold |
citations | 5 | |
popularity | Top 10% | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.3934/cpaa.2020021&type=result"></script>');
-->
</script>
handle: 10272/20904 , 10459.1/65974
In this work is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. The analytic integrability problem is characterized via the existence of a formal inverse integrating factor. The relation between the analytic integrability and the existence of an algebraic inverse integrating factor is also given. The first and second authors are partially supported by a MINECO/FEDER grant number MTM2014-56272-C2-2 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2017-84383-P and by an AGAUR (Generalitat de Catalunya) grant number 2017SRG 1276.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.cnsns.2018.09.018&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 5 | |
popularity | Top 10% | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.cnsns.2018.09.018&type=result"></script>');
-->
</script>
handle: 10272/22629
We consider the two-dimensional autonomous systems of differential equations where the origin is a monodromic degenerate singular point, i.e., with null linear part. In this work we give two heuristic procedures to obtain some center conditions (perhaps not necessary) for certain degenerate centers at the origin although they have characteristic directions.(c) 2023 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation The first two authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I+D+I co-financed with FEDER funds, in the frameof theproject PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276,P12-FQM-1658,UHU126150andP2000764).The author is partially supported by the Agencia Estatal de Investigación grant PID2020-113758GB-I00andanAGAUR (Generalitat de Catalunya) grant number2021SGR01618 Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.matcom.2023.07.006&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 2 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.matcom.2023.07.006&type=result"></script>');
-->
</script>
handle: 10459.1/59434
In this paper, we use a geometric criterium based on the classical method of the construction of Lyapunov functions to determine if a differential system has a focus or a center at a singular point. This criterium is proved to be useful for several examples studied in previous works with other more specific methods.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/s00009-015-0641-0&type=result"></script>');
-->
</script>
hybrid |
citations | 12 | |
popularity | Top 10% | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1007/s00009-015-0641-0&type=result"></script>');
-->
</script>
handle: 10272/20905 , 10459.1/58412
In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a Hamiltonian system. It is shown how difficult is the integrability problem even inside this simple family of degenerate centers or perturbations of them. The first and third authors are supported by a MINECO/FEDER grant number MTM2010-20907-C02-02 and by the Consejer´ıa de Educaci´on y Ciencia de la Junta de Andaluc´ıa (projects P12-FQM-1658, FQM-276). The fourth author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by a AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.nonrwa.2016.02.003&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 7 | |
popularity | Top 10% | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.nonrwa.2016.02.003&type=result"></script>');
-->
</script>
handle: 10272/20445
We characterize, using normal forms of quasi-homogeneous expansions, the analytic vector fields at nilpotent singular point having an algebraic first integral over the ring C [[ x, y ]] . As a consequence, we provide a link between the algebraic integrability problem and the existence of a formal inverse integrat- ing factor which is null at the singular point. This work has been partially supported by Ministerio de Ciencia, Innovación y Universidades, Spain (project PGC2018-096265-BI00) and by Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía, Spain (projects FQM-276, UHU-1260150 and P12-FQM-1658 Funding for open access charge: Universidad de Huelva / CBUA. Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.chaos.2021.110765&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 0 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.chaos.2021.110765&type=result"></script>');
-->
</script>
Altres ajuts: Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276) In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i.e. in the problem of distinguishing between a focus and a center.
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2020.111746&type=result"></script>');
-->
</script>
Green | |
bronze |
citations | 1 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2020.111746&type=result"></script>');
-->
</script>
handle: 10272/23306
The first three authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I +D+I co-financed with FEDER funds, in the frame of the project PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276, P12-FQM-1658, UHU126150 and P20 00764). The last author is partially supported by the Agencia Estatal de Investigación, Spain grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618. For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term. Departamento de Matemáticas
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2023.113304&type=result"></script>');
-->
</script>
Green | |
hybrid |
citations | 1 | |
popularity | Average | |
influence | Average | |
impulse | Average |
<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=10.1016/j.na.2023.113304&type=result"></script>');
-->
</script>
handle: 10459.1/65973
In this work it is solved the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions.