CYCLES AND SUNSPOTS - THE POINCARE-HOPF APPROACH

This paper deals with the existence of stationary sunspot equilibria ( SSE) of finite order in an n-commodity economy. We first provide a sim ple condition that is sufficient for the existence of SSE associated w ith any given Markov matrix. This condition encompasses and extends pr evious results by Guesnerie (Journal of Economic Theory, 1986, 40, 103 -128) and Chiappori and Guesnerie(in: Economic complexity, chaos, suns pots, bubbles and nonlinearity, 189, CUP). Also, we consider the order of the corresponding SSE(i.e. the cardinality of their support), and we show that almost all of these are of maximum order. Finally, we stu dy the links between SSE and cycles, and find that the existence of cy cles of order 2 detected by our condition implies that of SSE arbitrar ily close to cycles of order k for any even k - although cycles of ord er k may not exist in such models.