This volume contains the proceedings of the East Asia Joint Symposium on Fields and Strings 2021, held at the Media Center of Osaka City University on November 22-27, 2021. About 160 physicists from all over East Asia attended physically or joined online this symposium and more than 50 researchers presented their results in the invited lectures, the short talks or the poster session. Quantum field theory and string theory in the context of several exciting developments were discussed, which include frontiers of supersymmetric gauge theory, anomalies and higher form symmetries, and several issues on quantum gravity and black holes.

Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows). Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described. The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of interest to specialists in dynamical systems and their applications.