He and Benoit Mandelbrot were the recipients of the 2003 Japan Prize in Science and Technology: Yorke was selected for his work in chaotic systems.

[2] He received the Doctor Honoris Causa degree from the Universidad Rey Juan Carlos, Madrid, Spain, in January 2014.

Li coined the mathematical term chaos in a paper they published in 1975 entitled Period three implies chaos,[6] in which it was proved that every one-dimensional continuous map that has a period-3 orbit must have two properties: (1) For each positive integer p, there is a point in R that returns to where it started after p applications of the map and not before.

He and his colleagues (Edward Ott and Celso Grebogi) had shown with a numerical example that one can convert a chaotic motion into a periodic one by a proper time-dependent perturbation of the parameter.

Together with Kathleen T. Alligood and Tim D. Sauer, he was the author of the book Chaos: An Introduction to Dynamical Systems.