Analytical complexity: Development of the topicстатья
Статья опубликована в журнале из списка RSCI Web of Science
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Дата последнего поиска статьи во внешних источниках: 7 декабря 2013 г.
Аннотация:The complexity of analytic functions of two variables is studied in terms of the
order of complexity suggested in [1]. This paper continues [1]. An estimate for the complexity
of a polynomial using its degree is given. Examples of homogeneous and harmonic functions
are treated. An estimate for the complexity of a power series in terms of the geometry of
the support of the series is given. Differential equations defining classes of complexity are
considered. For polynomial mappings of complexity one, the Jacobian conjecture is proved.
In this connection, the complexity of mappings of the plane is discussed.