Noncommutative dynamical systems with two generators and their applications in analysis

Boris Paneah
2003 Discrete and Continuous Dynamical Systems. Series A  
In this paper, some new dynamical systems which are determined by a semigroup Φ of maps in a closed interval I are studied.The main peculiarity of these systems is that Φ is generated by two noncommuting maps. Introducing certain closed subsets T 1 and T 2 in I makes it possible to determine some specific orbits corresponding to Φ and some specific attractors in I. These orbits play a crucial role in solving a wide variety problems in such diverse fields of analysis as functional and
more » ... onal and functional-integral equations, integral geometry, boundary problems for hyperbolic partial differential equations of higher (> 2) order. In the first part of this work we describe some conditions which ensure the existence of attractors in question of a special structure. In the second part several new problems in the above-mentioned fields of analysis are formulated, and we trace how the above dynamic approach works in solving this problems. 1991 Mathematics Subject Classification. 37N99, 39B22, 35L35.
doi:10.3934/dcds.2003.9.1411 fatcat:rfe6ouegkbh7dkpgvgh6nur3fm