Abstract
The problem of the existence of quadratic forms that have a positive definite derivative along the solutions of linear extensions of dynamical systems on a torus is considered. Assuming the existence of quadratic forms whose derivative is positive definite only with respect to part of the variables, conditions ensuring the existence of a quadratic form whose derivative is already positive definite with respect to all variables are found.
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Literature cited
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1713–1717, December, 1990.
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Kulik, V.L. Existence of Lyapunov functions of variable sign for linear extensions of dynamical systems on a torus. Ukr Math J 42, 1548–1552 (1990). https://doi.org/10.1007/BF01060829
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DOI: https://doi.org/10.1007/BF01060829