IJPAM: Volume 70, No. 2 (2011)
UNDER -MODAL MAPS
Department of Mathematics
University of Evora
Rua Romao Ramalho, 59, Evora, 7000-671, PORTUGAL
Abstract. We consider the dynamical system , where is a class of differentiable real functions defined on some interval and is an operator , where is a function on the real line. In this work we introduce and develop some techniques of symbolic dynamics for the dynamical system . We analyze in detail the case in which arises from a differentiable -modal map . In this case we obtain a combinatorial description of the orbits of which depends on the combinatorial description of the orbits of one dimensional dynamical system induced by on the interval.
Received: February 10, 2011
AMS Subject Classification: 37B10, 39B12, 37C05, 26A18
Key Words and Phrases: symbolic dynamics, infinite dimensional dynamical systems, -modal maps, iteration theory
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395