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This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles.Many economic theories have analyzed cyclical behaviors of economic variables.

It also covers some advanced frameworks such as repeated games with non-simultaneous moves, repeated games with overlapping generations, global games, and voluntarily separable repeated prisoner's dilemma, so that readers familiar with basic game theory can expand their knowledge.

This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson-Solow-Srinivasan (RSS) model. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model.

This book is devoted to the study of two large classes of discrete-time optimal control problems arising in mathematical economics. Nonautonomous optimal control problems of the first class are determined by a sequence of objective functions and sequence of constraint maps. They correspond to a general model of economic growth. We are interested in turnpike properties of approximate solutions and in the stability of the turnpike phenomenon under small perturbations of objective functions and constraint maps. The second class of autonomous optimal control problems  corresponds to another general class of models of economic dynamics which  includes the Robinson-Solow-Srinivasan  model as a particular case. In Chap. 1 we discuss turnpike properties for a large class  of discrete-time optimal control problems studied in the literature and for the Robinson-Solow-Srinivasan model. In Chap. 2 we introduce the first class of optimal control problems and study its turnpike property. This class of problems is also discussed in Chaps. 3-6. In Chap. 3 we study the stability of the turnpike phenomenon under small perturbations of the objective functions. Analogous results for problems with discounting are considered in Chap. 4. In Chap. 5 we study the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. Analogous results for problems with discounting are established in Chap. 6. The results of Chaps. 5 and 6 are new. The second class of problems is studied in Chaps. 7-9. In Chap. 7 we study the turnpike properties.  The stability of the turnpike phenomenon under small perturbations of the objective functions is established in Chap. 8. In  Chap. 9 we establish the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. The results of Chaps. 8 and 9 are new. In Chap. 10 we study optimal control problems related to a model of knowledge-based endogenous economic growth and show  the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.

This volume is devoted to a reappraisal of the Marginal Revolution on the occasion of its 150th anniversary.The year 1871 should be remembered as one of the most important turning points in the history of economics. W. S. Jevons, C. Menger, and L. Walras published epochal works at the very beginning of the 1870s. Although these works were written independently, they shared a common mathematical structure based on classical analysis. For this reason, the emergence of the trio is called the Marginal Revolution. Indeed, 1871 is the starting point of modern economics in the proper sense.In 1971, several academic conferences were held on the occasion of the 100th anniversary of the Revolution, which exerted the stimulating influence upon the historical researches into the Revolution. Now more than fifty years have passed since then. Economic theory has experienced further substantial changes in researchers¿ central interest, the way of reasonings and the styles of description during this period. In view of the new achievements acquired in recent fifty years, it seems an indispensable task for us to review and reevaluate the Marginal Revolution based upon the present status of economics.We also keep in mind that some concepts and doctrines once discarded could reappear in a later stage of history in a more or less transfigured form.The introductory chapter will be a guide for readers not only from the economics community but also from the mathematics community.