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Lie-point symmetries in bifurcation problems
1992The authors develop a theory of bifurcations of differential equations with Lie point symmetries. Viewing the differential equation as an ``algebraic equation'' on some jet bundle is the key of the analysis. The authors show how the well-known results of equivariant bifurcation theory can be formulated in this context and how the results carry over ...
CICOGNA, GIAMPAOLO, Gaeta G.
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Groups, Lie Algebras, Symmetries in Physics
2018The first problems in this chapter deal with basic properties of groups and of group representations. Fundamental results following from Schur lemma are introduced since the beginning in the case of finite groups, with simple applications of character theory, in the study of vibrational levels of symmetric systems. Other problems concern the notion and
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Lie symmetries of nonlinear systems with unknown inputs
Mechanical Systems and Signal Processing, 2023Xiaodong Shi, Manolis Chatzis
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Lie symmetry analysis and exact solutions of the time-fractional biological population model
Physica A: Statistical Mechanics and Its Applications, 2020Zhi-Yong Zhang
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Review of symbolic software for lie symmetry analysis
Mathematical and Computer Modelling, 1997Willy A Hereman
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Perturbation to Lie symmetry and adiabatic invariants for Birkhoffian systems on time scales
Communications in Nonlinear Science and Numerical Simulation, 2019exaly