Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Time-Reversibility and Ivariants of Some 3-dim Systems
Authors: Tatjana Petek and Valery G. Romanovski
Keywords: Integrability, invariants, reversibility, polynomial systems of ODEs
– 0.16 Mb
Keywords: Integrability, invariants, reversibility, polynomial systems of ODEs
Abstract
We study time-reversibility and invariants of the group of transformations $x\to x, \ y\to \alpha y, \ z \to \alpha ^{-1}z$ for three-dimensional polynomial systems with $0:1:-1$ resonant singular point at the origin. An algorithm to find the Zariski closure of the set of time-reversible systems in the space of parameters is proposed. The interconnection of time-reversibility and invariants of the group mentioned above is discussed.Tatjana Petek
Faculty of Electrical Engineering and Computer Science,
University of Maribor, Koroška cesta 46, SI-2000 Maribor,
Slovenia
Institute of Mathematics, Physics and Mechanics,
Jadranska 19, SI-1000 Ljubljana, Slovenia
E-mail:
Valery G. Romanovski
Faculty of Electrical Engineering and Computer Science,
University of Maribor, Koroška cesta 46, SI-2000 Maribor,
Slovenia
Center for Applied Mathematics and Theoretical Physics,
Mladinska 3, SI-2000 Maribor, Slovenia
Faculty of Natural Science and Mathematics, University of
Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
E-mail:
Faculty of Electrical Engineering and Computer Science,
University of Maribor, Koroška cesta 46, SI-2000 Maribor,
Slovenia
Institute of Mathematics, Physics and Mechanics,
Jadranska 19, SI-1000 Ljubljana, Slovenia
E-mail:
Valery G. Romanovski
Faculty of Electrical Engineering and Computer Science,
University of Maribor, Koroška cesta 46, SI-2000 Maribor,
Slovenia
Center for Applied Mathematics and Theoretical Physics,
Mladinska 3, SI-2000 Maribor, Slovenia
Faculty of Natural Science and Mathematics, University of
Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i1.p16Fulltext
– 0.16 Mb
Contents
- Criteria for the nonexistence of periodic orbits in planar differential systems
- Some families of quadratic systems with at most one limit cycle
- Time-Reversibility and Ivariants of Some 3-dim Systems
- A survey on local integrability and its regularity
- The bifurcation diagram of the configurations of invariant lines of total multiplicity exactly three in quadratic vector fields
- Counting configurations of limit cycles and centers
