Yantır, Burcu Silindir2016-01-082016-01-082009http://hdl.handle.net/11693/14860Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Ph.D.) -- Bilkent University, 2009.Includes bibliographical references leaves 98-102.We present two approaches to unify the integrable systems. Both approaches are based on the classical R-matrix formalism. The first approach proceeds from the construction of (1 + 1)-dimensional integrable ∆-differential systems on regular time scales together with bi-Hamiltonian structures and conserved quantities. The second approach is established upon the general framework of integrable discrete systems on R and integrable dispersionless systems. We discuss the deformation quantization scheme for the dispersionless systems. We also apply the theories presented in this dissertation, to several well-known examples.viii, 102 leavesEnglishinfo:eu-repo/semantics/openAccessIntegrable systemsregular time scaleR-matrix formalismbiHamiltonian structuresconserved quantitiesdispersionless systemsdeformation quantization schemeQA614.8 .Y35 2009Differentiable dynamical systems.Hamiltonian systems.Thesis