Preface In th e fortie s P . Ya . Polubarinova-Kochin a an d P . P . Kufare v studie d the problem o f evolutio n o f a round oi l spot surrounde d b y water when oi l is extracte d fro m a wel l insid e th e spo t (Figur e 1) . I t turne d ou t tha t th e boundary of the spot remains an algebraic curve of degree four i n the course of evolution . Thi s curv e i s th e imag e o f a n ellips e unde r a reflectio n wit h respect to a circle. I n 195 0 Kufarev manage d t o generalize this property: i f initially th e oi l spo t i s th e imag e o f th e uni t dis k unde r a conforma l ma p given b y a rationa l functio n o f th e comple x coordinat e i n th e disk , the n i t retains this property in the course of evolution . In 197 2 S. Richardson foun d a n infinite serie s of first integrals of motio n of th e spot . H e proved tha t th e integra l o f an y harmonic functio n ove r th e oil domain change s linearly i n time. Thi s allowed Richardson t o give a new proof o f th e invarianc e o f rationalit y an d a n effectiv e metho d t o construc t explicit solutions . FIGURE 1 vii

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