LEADER 05212nam 2200685Ia 450 001 9910822863803321 005 20230120010030.0 010 $a1-281-76362-4 010 $a9786611763626 010 $a0-08-087376-6 035 $a(CKB)1000000000554024 035 $a(EBL)404189 035 $a(OCoLC)476217324 035 $a(SSID)ssj0000138885 035 $a(PQKBManifestationID)11136578 035 $a(PQKBTitleCode)TC0000138885 035 $a(PQKBWorkID)10101193 035 $a(PQKB)11007181 035 $a(MiAaPQ)EBC404189 035 $a(EXLCZ)991000000000554024 100 $a20731217d1974 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential equations, dynamical systems, and linear algebra /$fMorris W. Hirsch and Stephen Smale 210 $aNew York $cAcademic Press$d1974 215 $a1 online resource (373 p.) 225 1 $aPure and applied mathematics ;$vv. 60 300 $aDescription based upon print version of record. 311 $a0-12-349550-4 320 $aIncludes bibliographical references. 327 $aFront Cover; Differential Equations, Dynamical Systems, and Linear Algebra; Copyright Page; Contents; Preface; CHAPTER 1. FIRST EXAMPLES; 1. The Simplest Examples; 2. Linear Systems with Constant Coefficients; Notes; CHAPTER 2. NEWTON'S EQUATION AND KEPLER'S LAW; 1. Harmonic Oscillators; 2. Some Calculus Background; 3. Conservative Force Fields; 4. Central Force Fields; 5. States; 6. Elliptical Planetary Orbits; Notes; CHAPTER 3. LINEAR SYSTEMS WITH CONSTANT COEFICIENTS AND REAL EIGENVALUES; 1. Basic Linear Algebra; 2. Real Eigenvalues 327 $a3. Differential Equations with Real, Distinct Eigenvalues4. Complex Eigenvalues; CHAPTER 4. LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS AND COMPLEX EIGENVALUES; 1. Complex Vector Spaces; 2. Real Operators with Complex Eigenvalues; 3. Application of Complex Linear Algebra to Differential Equations; CHAPTER 5. LINEAR SYSTEMS AND EXPONENTIALS OF OPERATORS; 1. Review of Topology in Rn; 2. New Norms for Old; 3. Exponentials of Operators; 4. Homogeneous Linear Systems; 5. A Nonhomogeneous Equation; 6. Higher Order Systems; Notes; CHAPTER 6. LINEAR SYSTEMS AND CANONICAL FORMS OF OPERATORS 327 $a1. The Primary Decomposition2. The S + N Decomposition; 3. Nilpotent Canonical Forms; 4. Jordan and Real Canonical Forms; 5. Canonical Forms and Differential Equations; 6. Higher Order Linear Equations; 7. Operators on Function Spaces; CHAPTER 7. CONTRACTIONS AND GENERIC PROPERTIES OF OPERATORS; 1. Sinks and Sources; 2. Hyperbolic Flows; 3. Generic Properties of Operators; 4. The Significance of Genericity; CHAPTER 8. FUNDAMENTAL THEORY; 1. Dynamical Systems and Vector Fields; 2. The Fundamental Theorem; 3. Existence and Uniqueness; 4. Continuity of Solutions in Initial Conditions 327 $a5. On Extending Solutions6. Global Solutions; 7. The Flow of a Differential Equation; Notes; CHAPTER 9. STABILITY OF EQUILIBRIA; 1. Nonlinear Sinks; 2. Stability; 3. Liapunov Functions; 4. Gradient Systems; 5. Gradients and Inner Products; Notes; CHAPTER 10. DIFFERENTIAL EQUATIONS FOR ELECTRICAL CIRCUITS; 1. An RLC Circuit; 2. Analysis of the Circuit Equations; 3. Van der Pol's Equation; 4. Hopf Bifurcation; 5. More General Circuit Equations; Notes; CHAPTER 11. THE POINCARE?-BENDIXSON THEOREM; 1. Limit Sets; 2. Local Sections and Flow Boxes; 3. Monotone Sequences in Planar Dynamical Systems 327 $a4. The Poincare?-Bendixson Theorem5. Applications of the Poincare?-Bendixson Theorem; Notes; CHAPTER 12. ECOLOGY; 1. One Species; 2. Predator and Prey; 3. Competing Species; Notes; CHAPTER 13. PERIODIC ATTRACTORS; 1. Asymptotic Stability of Closed Orbits; 2. Discrete Dynamical Systems; 3. Stability and Closed Orbits; CHAPTER 14. CLASSICAL MECHANICS; 1. The n-Body Problem; 2. Hamiltonian Mechanics; Notes; CHAPTER 15. NONAUTONOMOUS EQUATIONS AND DIFFERENTIABILITY OF FLOWS; 1. Existence, Uniqueness, and Continuity for Nonautonomous Differential Equations 327 $a2. Differentiability of the Flow of Autonomous Equations 330 $aThis book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject. 410 0$aPure and applied mathematics (Academic Press) ;$v60. 606 $aDifferential equations 606 $aAlgebras, Linear 615 0$aDifferential equations. 615 0$aAlgebras, Linear. 676 $a510.8 s515.35 676 $a510/.8 s 515/.35 676 $a512.5 676 $a515.35 676 $a515/.35 700 $aHirsch$b Morris W.$f1933-$013761 701 $aSmale$b Stephen$f1930-$031836 701 $aHirsch$b Morris W.$f1933-$013761 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910822863803321 996 $aDifferential equations, dynamical systems and linear algebra$9348983 997 $aUNINA