Dynamical chaos: the difficult path discovering

Dynamic chaos - a remarkable milestone development of science of the last century - has attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world. What features of the development of science, economic and social conditions led to that long and difficult path of discovery of chaos began precisely at the end of the XIX century and stretched out for decades? Finding answers to these questions is the subject of this paper.