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The problem of cosmological expansion on small scales (e.g., inside the planetary systems) has a long history, dating back to the papers by C.G. McVittie from 1932 and 1933, and quite a large number of researchers dealt with this topic in the subsequent few decades. Although most of them concluded that the Hubble expansion should be strongly suppressed at small distances, there is no commonly-established criterion for such suppression at present and, moreover, the various estimates of the Hubble expansion often contradict each other. Besides, there is some indirect evidence that cosmological expansion might be important, for example, in the long-term evolution of the Solar system. So, it is timely to gather the specialists from different disciplines, ranging from planetology to galaxy evolution, to discuss the problem of local cosmological influences from various points of view, both theoretical and observational.