REFLEXIVE MAPPINGS AND NONLINEAR DYNAMICS A.G. Chkhartishvili 1 , D.A. Novikov 2 sandro_ch@mail.ru , novikov@ipu.ru 1 Moscow State University, 2 Institute of Control Sciences RAS The paper considers reflexive mappings properties: it is proved that, when the agents in the framework of the game-theoretic model make their decisions on the base of the finite informa- tional structures, actions, chosen by phantom agents, are defined by the system of nonlinear iterated mappings [1]. Exploration of the model allows concluding that the informational equi- librium is generally unstable under the increase of the reflexivity depth. Consider the informational structure I = (I 1 , I 2 , …, I n ), where I i = (q i , q ij , q ijk , …), i, j, k ˛ N = {1, 2, .., n}, is the informational structure of i-th agent, i ˛ N, q i ˛ W state of nature, q ij ˛ W – his beliefs about the beliefs of j-th agent, q ijk ˛ W – his beliefs about the beliefs of j-th agent about the beliefs of k-th agent and so on ad infinitum [2]. Reflexive game is the "normal form" game {N, (A i ) i ˛ N , (f i ()) i ˛ N , I}, where N is the set of players (agents), A i is the set of i-th agent feasible actions, f i (): W · A' fi ´ 1 – his goal function, A' =  ˛N i i A , i ˛ N, I – informational struc- ture.