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This paper studies stability properties of the trivial invariant torus of a class of nonlinear extensions of dynamical systems on torus. Two theorems on exponential stability and instability of the invariant torus in terms of quadratic forms that are sign-definite in nonwandering set of the dynamical system have been proven. 2010 Mathematics Subject Classification: 34C46; 34C45; 34D35

Stability of trivial torus of nonlinear multifrequency systems via sign-definite quadratic forms