04059nam 2200733 a 450 991114944720332120251116183507.097866131445919781283144599128314459X97898143077589814307750(CKB)3360000000001383(EBL)731209(OCoLC)740446113(SSID)ssj0000520625(PQKBManifestationID)11364259(PQKBTitleCode)TC0000520625(PQKBWorkID)10514927(PQKB)10171788(MiAaPQ)EBC731209(WSP)00001109 (Au-PeEL)EBL731209(CaPaEBR)ebr10479795(CaONFJC)MIL314459(Perlego)850174(EXLCZ)99336000000000138320110225d2010 uy 0engur|n|---|||||txtccr2-D quadratic maps and 3-D ODE systems a rigorous approach /Elhadj Zeraoulia, Julien Clinton Sprott1st ed.Singapore ;Hackensack, N.J. World Scientific Pub. Co.c20101 online resource (342 p.)World Scientific series on nonlinear science. Series A, Monographs and treatises,1793-1010 ;v. 73Description based upon print version of record.9789814307741 9814307742 Includes bibliographical references and index.Preface; Contents; Acknowledgements; 1. Tools for the rigorous proof of chaos and bifurcations; 2. 2-D quadratic maps: The invertible case; 3. Classification of chaotic orbits of the general 2-D quadratic map; 4. Rigorous proof of chaos in the double-scroll system; 5. Rigorous analysis of bifurcation phenomena; Bibliography; IndexThis book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the H�non map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters. Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward H�non mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincare map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincare mapping in addition to other analytical methods.World Scientific series on nonlinear science.Series A,Monographs and treatises ;v. 73.Forms, QuadraticDifferential equations, LinearBifurcation theoryDifferentiable dynamical systemsProof theoryForms, Quadratic.Differential equations, Linear.Bifurcation theory.Differentiable dynamical systems.Proof theory.515.352Zeraoulia ElhadjSprott Julien CMiAaPQMiAaPQMiAaPQBOOK9911149447203321UNINA03648nam 22004695 450 991112745350332120260820143711.0978365850459510.1007/978-3-658-50459-5(CKB)50429815700041(DE-He213)978-3-658-50459-5(MiAaPQ)EBC32972978(Au-PeEL)EBL32972978(EXLCZ)995042981570004120260730d2026 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierLinear and Nonlinear FEM An Introduction with Applications in Sheet Metal Forming Simulation with LS-DYNA® /by Marcus Wagner1st ed. 2026.Wiesbaden :Springer Fachmedien Wiesbaden :Imprint: Springer,2026.1 online resource (XIV, 408 p. 268 illus.)131 illus. in colorEngineering Series9783658504588 Introduction to Linear FEM -- Mechanical Quantities of Structural Mechanics -- Mathematical Model Based on Energy Principles -- Discretization Using Finite Elements -- Finite Element Classes -- Mathematical and Numerical Aspects of the FEM -- Linear time-dependent FEM -- Geometric Nonlinearity -- Material Nonlinearity -- Contact Modeling -- Solution of Nonlinear Static Problems -- Time Integration of Nonlinear Dynamic Problems -- Sheet Metal Forming Simulation -- Appendix: Mathematical Tools -- Introduction to Simulation with LS-DYNA® -- Solutiuons to Exercises.This textbook provides a clear and accessible introduction to the characteristics and properties of linear finite elements in the fields of elastostatics and dynamics, and explains the procedures involved in building simulation models. The second part focuses on nonlinear, time-dependent phenomena and their corresponding solution methods. Practical examples from sheet metal forming are illustrated using the LS-DYNA® software. The emphasis is placed on explaining the interrelationships essential for users of commercial simulation software. Theoretical fundamentals are presented to the extent required for understanding how to use such programs effectively. The content Introduction to Linear FEM – Mechanical Quantities of Structural Mechanics – Mathematical Model Based on Energy Principles – Discretization Using Finite Elements – Finite Element Classes – Mathematical and Numerical Aspects of the FEM – Linear time-dependent FEM – Geometric Nonlinearity – Material Nonlinearity – Contact Modeling – Solution of Nonlinear Static Problems – Time Integration of Nonlinear Dynamic Problems – Sheet Metal Forming Simulation – Appendix: Mathematical Tools – Introduction to Simulation with LS-DYNA® – Solutiuons to Exercises Target groups Students from bachelor's and master's degree courses in engineering at colleges and technical universities Engineers and technicians The author Prof. Dr.-Ing. Marcus Wagner teaches finite elements, engineering informatics and machine dynamics at the OTH Regensburg, Germany and heads the finite element and machine dynamics laboratories.Engineering SeriesEngineering designEngineering DesignEngineering design.Engineering Design.620.0042Wagner Marcusauthttp://id.loc.gov/vocabulary/relators/aut1127413MiAaPQMiAaPQMiAaPQBOOK9911127453503321Linear and Nonlinear FEM4844900UNINA