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Linear chaos
416
Nonlinear
science
abstracts
Steklov Mathematical THE QUANTUM NONLINEAR a-MODEL, L. D. Faddeev, Institute. The reduction of the quantum nonlinear u-model to the tensor product This permits to calculate of two Heisenberg KXX ferromagnetics has been found. the mass spectrum and the S matrix of the model.
End of Workshop Abstracts
371
(M2,T8) MAXIMAL AND MINIMAL SOLUTIONS TO A CLASS OF ELLIPTIC QUASI-LINEAR “G . PROBLEMS, Giovanni Maria Groianiello, Istituto Matematico Castelnuovo", Universita di Roma, Rome 00100, ITALY. We prove existence of maximal and minimal solutions to bilateral problems for quasilinear elliptic operators with nondivergence principal part independent of the gradient. This result also covers the case of equations, when the obstacles can be taken as lower and upper solutions. JOURNAL: Proceedings AMS 372 (Ml,M2) LINEAR CHAOS, 0. E. Rossler, Institute for Physical and Theoretical Chemistry, University of Tubingen, 7400 Tubingen, WEST GERMANY; J. J. Kozak, Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556, USA; D. Hoffmann, University of Tubingen, WEST GERMANY. Three types of linear chaos are proposed for consideration. i) the Poincare-Carleman linear transform of a given nonlinear ordinary differential equation, in the case the latter is chaotic. ii) The infinite classical harmonic placed impurity (Cukier-Mazur) in the case chain with a heavy, asymmetrically strong mixing is generated. iii) The classical wave equation subjected to a finite two-dimensional domain with a reflection boundary shaped like a billiard table, in the case the latter generates billiard chaos (normals-of-the-waves The first two examples involve countably many linear variables, the chaos). Genuine (infinite number of variables) linear third implies uncountably many. chaos is of interest also because of the implied existence of finite linear finite-n over Therefore, approximate it finite times. systems that "quasiperiodic computers" of a similar standing as finite-state machines appear Quantum mechanical systems (like those studied by Davidson and Kozak) to exist. form a natural subclass. VII. Sitges conference; 2. Naturforsch. A JOURNAL: THE PERIODICALLY KICKED ROTATOR: RECURRENCE AND/OR ENERGY GROWTH, (P8,12) B. Dorizzi, B. Grammaticos, CNET, Departement de Mathematiques, 92 Issy les Moulineaux, FRANCE; Y. Pomeau, SPh.T, CEN Saclay, 91191, Gif-surde Physique de l'ENS, 24 rue Yvette. Cedex, France and Laboratoire Lhomond, 75005 Paris, FRANCE. Its We explore the properties of the quantum kicked rotator. Its behavior, as found by computer classical equivalent being the standard map. At low studies, depends very much on the strength of the external forcing. However strength it is seemingly recurrent in the sense of Hogg and Huberman. For quantum systems, a unitary its energy increases with time at large forcings. 373
Nonlinear
science
abstracts
Steklov Mathematical THE QUANTUM NONLINEAR a-MODEL, L. D. Faddeev, Institute. The reduction of the quantum nonlinear u-model to the tensor product This permits to calculate of two Heisenberg KXX ferromagnetics has been found. the mass spectrum and the S matrix of the model.
End of Workshop Abstracts
371
(M2,T8) MAXIMAL AND MINIMAL SOLUTIONS TO A CLASS OF ELLIPTIC QUASI-LINEAR “G . PROBLEMS, Giovanni Maria Groianiello, Istituto Matematico Castelnuovo", Universita di Roma, Rome 00100, ITALY. We prove existence of maximal and minimal solutions to bilateral problems for quasilinear elliptic operators with nondivergence principal part independent of the gradient. This result also covers the case of equations, when the obstacles can be taken as lower and upper solutions. JOURNAL: Proceedings AMS 372 (Ml,M2) LINEAR CHAOS, 0. E. Rossler, Institute for Physical and Theoretical Chemistry, University of Tubingen, 7400 Tubingen, WEST GERMANY; J. J. Kozak, Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556, USA; D. Hoffmann, University of Tubingen, WEST GERMANY. Three types of linear chaos are proposed for consideration. i) the Poincare-Carleman linear transform of a given nonlinear ordinary differential equation, in the case the latter is chaotic. ii) The infinite classical harmonic placed impurity (Cukier-Mazur) in the case chain with a heavy, asymmetrically strong mixing is generated. iii) The classical wave equation subjected to a finite two-dimensional domain with a reflection boundary shaped like a billiard table, in the case the latter generates billiard chaos (normals-of-the-waves The first two examples involve countably many linear variables, the chaos). Genuine (infinite number of variables) linear third implies uncountably many. chaos is of interest also because of the implied existence of finite linear finite-n over Therefore, approximate it finite times. systems that "quasiperiodic computers" of a similar standing as finite-state machines appear Quantum mechanical systems (like those studied by Davidson and Kozak) to exist. form a natural subclass. VII. Sitges conference; 2. Naturforsch. A JOURNAL: THE PERIODICALLY KICKED ROTATOR: RECURRENCE AND/OR ENERGY GROWTH, (P8,12) B. Dorizzi, B. Grammaticos, CNET, Departement de Mathematiques, 92 Issy les Moulineaux, FRANCE; Y. Pomeau, SPh.T, CEN Saclay, 91191, Gif-surde Physique de l'ENS, 24 rue Yvette. Cedex, France and Laboratoire Lhomond, 75005 Paris, FRANCE. Its We explore the properties of the quantum kicked rotator. Its behavior, as found by computer classical equivalent being the standard map. At low studies, depends very much on the strength of the external forcing. However strength it is seemingly recurrent in the sense of Hogg and Huberman. For quantum systems, a unitary its energy increases with time at large forcings. 373