This US-Hungary Joint Fund research project on chaotic transients will be conducted by Dr. Peter Szepfalusy, Institute of Solid State Physics, Eotvos University, Budapest and Dr. Celso Grebogi, University of Maryland. Chaotic, unpredictable motion can be permanent or transient. In the latter case chaos can be observed on finite time scales only. The main objective of this research project is to improve understanding of transient chaos in both dissipative and Hamiltonian systems. The importance of investigating such chaotic transients lies in the fact that by analyzing the dynamics on finite time-scales, essential features like sensitive dependence on initial conditions and limited predictability of the process can be observed. The characterization of these transients is considered fundamental for the understanding of the dynamics. Results may lead to advances in applications in areas involving laser systems and nuclear or chemical reactions. This theoretical research in mathematics fulfills the US-Hungary Joint Fund program objective of advancing science by enabling leading experts in the United States and Hungary to combine complementary talents and pool research resources in areas of strong mutual interest and competence. Funds for the project are provided through the US-Hungary Joint Fund, Budapest, in accordance with established guidelines.