03197nam 22005535 450 991034932150332120200704183444.03-030-19373-X10.1007/978-3-030-19373-7(CKB)4100000009184973(DE-He213)978-3-030-19373-7(MiAaPQ)EBC5892517(PPN)269145087(EXLCZ)99410000000918497320190906d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierSymplectic Difference Systems: Oscillation and Spectral Theory /by Ondřej Došlý, Julia Elyseeva, Roman Šimon Hilscher1st ed. 2019.Cham :Springer International Publishing :Imprint: Birkhäuser,2019.1 online resource (XV, 593 p. 7 illus. in color.) Pathways in Mathematics,2367-34513-030-19372-1 Motivation and Preliminaries -- Basic Theory of Symplectic Systems -- Comparative Index Theory -- Oscillation Theory of Symplectic Systems -- Discrete Symplectic Eigenvalue Problems -- Miscellaneous Topics on Symplectic Systems.This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.Pathways in Mathematics,2367-3451Difference equationsFunctional equationsOperator theoryDifference and Functional Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12031Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Difference equations.Functional equations.Operator theory.Difference and Functional Equations.Operator Theory.515.625515.75515.45Došlý Ondřejauthttp://id.loc.gov/vocabulary/relators/aut499453Elyseeva Juliaauthttp://id.loc.gov/vocabulary/relators/autŠimon Hilscher Romanauthttp://id.loc.gov/vocabulary/relators/autBOOK9910349321503321Symplectic Difference Systems: Oscillation and Spectral Theory2499261UNINA02667nam 22005175 450 991030011730332120200705044616.03-319-92117-710.1007/978-3-319-92117-4(CKB)3810000000358848(DE-He213)978-3-319-92117-4(MiAaPQ)EBC5501045(PPN)229498108(EXLCZ)99381000000035884820180628d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierStructurally Unstable Quadratic Vector Fields of Codimension One /by Joan C. Artés, Jaume Llibre, Alex C. Rezende1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (VI, 267 p. 362 illus., 1 illus. in color.) 3-319-92116-9 Includes bibliographical references.Introduction -- Preliminary definitions -- Some preliminary tools -- A summary for the structurally stable quadratic vector fields -- Proof of Theorem 1.1(a) -- Proof of Theorem 1.1(b) -- Bibliography.Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors’ work on structurally stable planar quadratic polynomial differential systems. In the present work the authors aim at finding all possible phase portraits in the Poincaré disc, modulo limit cycles, of planar quadratic polynomial differential systems manifesting the simplest level of structural instability. They prove that there are at most 211 and at least 204 of them. .Differential equationsDynamicsErgodic theoryOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XDifferential equations.Dynamics.Ergodic theory.Ordinary Differential Equations.Dynamical Systems and Ergodic Theory.515.352Artés Joan Cauthttp://id.loc.gov/vocabulary/relators/aut501630Llibre Jaumeauthttp://id.loc.gov/vocabulary/relators/autRezende Alex Cauthttp://id.loc.gov/vocabulary/relators/autBOOK9910300117303321Structurally Unstable Quadratic Vector Fields of Codimension One1963844UNINA