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Dynamical system where proving chaos is equivalent to proving Fermat's conjecture |
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| Authors: | N C A da Costa F A Doria A F Furtado do Amaral |
| Institution: | (1) Institute for Advanced Studies, University of São Paulo, 05508 São Paulo SP, Brazil;(2) Research Center on Mathematical Theories of Communication, School of Communications, Federal University at Rio de Janeiro, 22290 Rio de Janeiro RJ, Brazil;(3) Institute of Physics, Federal University at Rio de Janeiro, 21940 Rio de Janeiro RJ, Brazil |
| Abstract: | We prove that we can explicitly construct the expression for a low-dimensional Hamiltonian system where proving the existence of a Smale horseshoe is equivalent to proving that Fermat's Conjecture is true. We then show that some sets of similar intractable problems are dense (in the usual topology) in the space of all dynamical systems over a finite-dimensional real manifold. |
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