Abstract: In terms of the non-linear dynamic characteristics of a tribological system, the research method of nonlinear theory should be used. In order to fully realize the nonlinear science theory of tribological research and make a quantitative study of complex tribological problems, the latest development of applications of the fractal geometry, chaos theory and wavelet theory in surface characterization, surface contact, wear particles identification, wear prediction, friction signal analysis and the dynamic description of wear process is introduced, and the application results are summarized. It is found that the fractal, chaos and wavelet theories are powerful tools for solving complicated tribological problems as well as effective methods of revealing the law of friction and wear and promoting the quantitative research of tribological problems.

Key words: Chaos, Fractal, Friction and wear, Tribology, Wavelet