Henri Poincaré and the qualitative theory of dynamic systems

The talk contains a brief overview of four memoirs of Poincaré "Sur les courbes définies par les équations différentielles " and his work " Nouvelles méthodes de mécanique céleste ", which together created the foundations of the qualitative theory of dynamic systems. The theorems of Poincaré – Bendixson and Poincaré – H. Hopf, as well as the bifurcation of Poincaré – Andronov – E. Hopf are considered. Poincaré's thoughts on the psychology of scientific creativity and his solicitude for the moral state of society also are mentioned.
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