Computability with low-dimensional dynamical systems
Theoretical Computer Science
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
Deciding stability and mortality of piecewise affine dynamical systems
Theoretical Computer Science
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
On undecidability bounds for matrix decision problems
Theoretical Computer Science
Computation in one-dimensional piecewise maps
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Periodic and infinite traces in matrix semigroups
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Lowering undecidability bounds for decision questions in matrices
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
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The computation in low-dimensional system is related to many long standing open problems. In this paper we show the universality of a one-dimensional iterative map defined by elementary functions. The computation in iterative maps have a number of connections with other unconventional models of computations. In particular, one-dimensional iterative maps can be simulated by a planar pseudo-billiard system. As a consequence of our main result we show that a planar pseudo-billiard system is not only can demonstrate a chaotic behaviour, but also has ability of universal computation.