O problemie trzech ciał, trajektoriach homoklinicznych i deterministycznym chaosie - Zawadzki, Henryk (About the problem of three bodies, homoclinic, trajectories and deterministic chaos, 2007)
J.H. Poincare (1854-1912), an outstanding French mathematician, astronomer, physicist and philosopher died long before the word “chaos” (in the sense of irregular, unpredictable behawior of trajectories of deterministic dynamical systems) appeared in mathematical literature. But many intuitions and results he obtained in his research in the field of differential equations and their applications in the modeling of celestial mechanics can be regarded as a part of chaos theory which arose in the second half of the twentieth century. In this article its author presents famous three-body problem of celestial mechanics and the Smale-Birkhoff homoclinic theorem, which gives sufficient conditions for existing of deterministic chaos in nonlinear dynamic systems.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2007; nr 1189, s. 18-24