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We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitelymany sinksnear the generic unfolding of a quadratic homoclinic tangency of adissipative saddle, can be perturbed along an infinite dimensional manifold of$C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously.On the other hand, if they are perturbed along one-parameter families thatunfold generically the quadratic tangencies, then at most a finite number ofthose sinks have continuation.

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency