caa a22 4500 469099720 CHVBK 20180323133041.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF00398809 doi (NATIONALLICENCE)springer-10.1007/BF00398809 Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem [Elektronische Daten] [Nalini Joshi, Damien Burtonclay, Rodney Halburd] Nonlinear nonautonomous discrete dynamical systems (DDS) whose continuum limits are the well-known Painlevé equations, have recently arisen in models of quantum gravity. The Painlevé equations are believed integrable because each is the isomonodromy condition for an associated linear differential equation. However, not every DDS with an integrable continuum limit is necessarily integrable. Which of the many discrete versions of the Painlevé equations inherit their integrability is not known. How to derive all their integrable discrete versions is also not known. We provide a systematic method of attacking these questions by giving a general discrete isomonodromy problem. Discrete versions of the first and second Painlevé equations are deduced from this general problem. Kluwer Academic Publishers, 1992 Joshi Nalini School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut Burtonclay Damien School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut Halburd Rodney School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut Letters in Mathematical Physics Kluwer Academic Publishers 26/2(1992-10-01), 123-131 0377-9017 26:2<123 1992 26 11005 https://doi.org/10.1007/BF00398809 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00398809 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Joshi Nalini School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut NATIONALLICENCE 700 1- Burtonclay Damien School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut NATIONALLICENCE 700 1- Halburd Rodney School of Mathematics, University of New South Wales, PO Box 1, 2033, Kensington, NSW, Australia aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 26/2(1992-10-01), 123-131 0377-9017 26:2<123 1992 26 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer