Education Sinergy in Research of Attractors and Basins of Nonlinear Mapping Attraction
Substantial constructs of nonlinear mappings of the plane on themselves made from homothetys, geometry of their attractors and basins of attraction in the context of manifestation of synergy effects in mathematical education are considered. Stages and the dialogue of mathematical, information, natural-science and humanitarian cultures are revealed during implementation of resource lessons on the basis of visual modeling. It is noted that in case of a research of complex systems and solutions of complex problems the important link is creation of hierarchy of evident models by updating bifurcation transitions to structures of higher organization orders. At the same time it is shown that mathematical education as a complex and open social system has a great potential of selforganization and positive manifestation of synergy effects in different directions: development and education of the personality, orderliness of the content and structure of cognitive experience, communication and social interaction of subjects on the basis of the dialogue of cultures, research activities as the integral attribute of modern education, the effective system of self-control of personality features of the student.