A counterexample to the hypothesis of V. I. Arnol'd regarding the proper vibrations of the membrane

It is shown that the hypothesis of transversality formulated by V. I. Arnol'd is not satisfied for all domains. Examples are presented of domains for which the variations of the eigenvalues of the Laplace operator for small perturbations of the domain are linearly dependent.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 51, pp. 134–137, 1975.