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We study the behaviour of one-dimensional strongly dissipative systemssubject to a quasi-periodic force. In particular we are interested in theexistence of response solutions, that is quasi-periodic solutions having thesame frequency vector as the forcing term. Earlier results available in theliterature show that, when the dissipation is large enough and a suitablefunction involving the forcing has a simple zero, response solutions can beproved to exist and to be attractive provided some Diophantine condition isassumed on the frequency vector. In this paper we show that the results extendto the case of arbitrary frequency vectors.

Response solutions for forced systems with large dissipation and arbitrary frequency vectors