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  • Produktbild: Delay Equations
  • Produktbild: Delay Equations
Band 110

Delay Equations Functional-, Complex-, and Nonlinear Analysis

Aus der Reihe Applied Mathematical Sciences

Fr. 191.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

23.07.2012

Abbildungen

XII, 536 p.

Verlag

Springer Us

Seitenzahl

536

Maße (L/B/H)

23.5/15.5/3 cm

Gewicht

826 g

Auflage

Softcover reprint of the original 1st edition 1995

Sprache

Englisch

ISBN

978-1-4612-8696-7

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

23.07.2012

Abbildungen

XII, 536 p.

Verlag

Springer Us

Seitenzahl

536

Maße (L/B/H)

23.5/15.5/3 cm

Gewicht

826 g

Auflage

Softcover reprint of the original 1st edition 1995

Sprache

Englisch

ISBN

978-1-4612-8696-7

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Delay Equations
  • Produktbild: Delay Equations
  • 0 Introduction and preview.- 0.1 An example of a retarded functional differential equation.- 0.2 Solution operators.- 0.3 Synopsis.- 0.4 A few remarks on history.- I Linear autonomous RFDE.- I.1 Prelude: a motivated introduction to functions of bounded variation.- I.2 Linear autonomous RFDE and renewal equations.- I.3 Solving renewal equations by Laplace transformation.- I.4 Estimates for det ?(z) and related quantities.- I.5 Asymptotic behaviour for t ? ?.- I.6 Comments.- II The shift semigroup.- II.1 Introduction.- II.2 The prototype problem.- II.3 The dual space.- II.4 The adjoint shift semigroup.- II.5 The adjoint generator and the sun subspace.- II.6 The prototype system.- II.7 Comments.- III Linear RFDE as bounded perturbations.- III.1 The basic idea, followed by a digression on weak* integration.- III.2 Bounded perturbations in the sun-reflexive case.- III.3 Perturbations with finite dimensional range.- III.4 Back to RFDE.- III.5 Interpretation of the adjoint semigroup.- III.6 Equivalent description of the dynamics.- III.7 Complexification.- III.8 Remarks about the non-sun-reflexive case.- III.9 Comments.- IV Spectral theory.- IV.1 Introduction.- IV.2 Spectral decomposition for eventually compact semigroups.- IV.3 Delay equations.- IV.4 Characteristic matrices, equivalence and Jordan chains.- IV.5 The semigroup action on spectral subspaces for delay equations.- IV.6 Comments.- V Completeness or small solutions?.- V.l Introduction.- V.2 Exponential type calculus.- V.3 Completeness.- V.4 Small solutions.- V.5 Precise estimates for ??(z)-1?.- V.6 Series expansions.- V.7 Lower bounds and the Newton polygon.- V.8 Noncompleteness, series expansions and examples.- V.9 Arbitrary kernels of bounded variation.- V.10 Comments.- VI Inhomogeneous linear systems.-VI.1 Introduction.- VI.2 Decomposition in the variation-of-constants formula.- VI.3 Forcing with finite dimensional range.- VI.4 RFDE.- VI.5 Comments.- VII Semiflows for nonlinear systems.- VII.1 Introduction.- VII.2 Semiflows.- VII.3 Solutions to abstract integral equations.- VII.4 Smoothness.- VII.5 Linearization at a stationary point.- VII.6 Autonomous RFDE.- VII.7 Comments.- VIII Behaviour near a hyperbolic equilibrium.- VIII.1 Introduction.- VIII.2 Spectral decomposition.- VIII.3 Bounded solutions of the inhomogeneous linear equation.- VIII.4 The unstable manifold.- VIII.5 Invariant wedges and instability.- VIII.6 The stable manifold.- VIII.7 Comments.- IX The center manifold.- IX.1 Introduction.- IX.2 Spectral decomposition.- IX.3 Bounded solutions of the inhomogeneous linear equation.- IX.4 Modification of the nonlinearity.- IX.5 A Lipschitz center manifold.- IX.6 Contractions on embedded Banach spaces.- IX.7 The center manifold is of class Ck.- IX.8 Dynamics on and near the center manifold.- IX.9 Parameter dependence.- IX.10 A double eigenvalue at zero.- IX.11 Comments.- X Hopf bifurcation.- X.l Introduction.- X.2 The Hopf bifurcation theorem.- X.3 The direction of bifurcation.- X.4 Comments.- XI Characteristic equations.- XI.1 Introduction: an impressionistic sketch.- XI.2 The region of stability in a parameter plane.- XI.3 Strips.- XI.4 Case studies.- XI.5 Comments.- XII Time-dependent linear systems.- XII.1 Introduction.- XII.2 Evolutionary systems.- XII.3 Time-dependent linear RFDE.- XII.4 Invariance of X?: a counterexample and a sufficient condition.- XII.5 Perturbations with finite dimensional range.- XII.6 Comments.- XIII Floquet Theory.- XIII.1 Introduction.- XIII.2 Preliminaries on periodicity and a stability result.- XIII.3 Floquet multipliers.-XIII.4 Floquet representation on eigenspaces.- XIII.5 Comments.- XIV Periodic orbits.- XIV.1 Introduction.- XIV.2 The Floquet multipliers of a periodic orbit.- XIV.3 Poincaré maps.- XIV.4 Poincaré maps and Floquet multipliers.- XIV.5 Comments.- XV The prototype equation for delayed negative feedback: periodic solutions.- XV.1 Delayed feedback.- XV.2 Smoothness and oscillation of solutions.- XV.3 Slowly oscillating solutions.- XV.4 The a priori estimate for unstable behaviour.- XV.5 Slowly oscillating solutions which grow away from zero, periodic solutions.- XV.6 Estimates, proof of Theorem 5.5(i) and (iii).- XV.7 The fixed-point index for retracts in Banach spaces, Whyburn’s lemma.- XV.8 Proof of Theorem 5.5(ii) and (iv).- XV.9 Comments.- XVI On the global dynamics of nonlinear autonomous differential delay equations.- XVI.1 Negative feedback.- XVI.2 A limiting case.- XVI.3 Chaotic dynamics in case of negative feedback.- XVI.4 Mixed feedback.- XVI.5 Some global results for general autonomous RFDE.- Appendices.- I Bounded variation, measure and integration.- I.1 Functions of bounded variation.- I.2 Abstract integration.- II Introduction to the theory of strongly continuous semigroups of bounded linear operators and their adjoints.- II. 1 Strongly continuous semigroups.- II.2 Interlude: absolute continuity.- II.3 Adjoint semigroups.- II.4 Spectral theory and asymptotic behaviour.- III The operational calculus.- III.1 Vector-valued functions.- III.2 Bounded operators.- III.3 Unbounded operators.- IV Smoothness of the substitution operator.- V Tangent vectors, Banach manifolds and transversality.- V.1 Tangent vectors of subsets of Banach spaces.- V.2 Banach manifolds.- V.3 Submanifolds and transversality.- VI Fixed points of parameterized contractions.- VII Linearage-dependent population growth: elaboration of some of the exercises.- VIII The Hopf bifurcation theorem.- References.- List of symbols.- List of notation.