MARC Record from marc_columbia

LEADER: 04296fam a2200409 a 4500
001 1253123
005 20220602003010.0
008 930122s1993 enk b 001 0 eng
010 $a 93009344
020 $a0521432154
020 $a0521437997 (pbk.)
035 $a(OCoLC)27432580
035 $a(OCoLC)ocm27432580
035 $9AGY5689CU
035 $a(NNC)1253123
035 $a1253123
040 $aDLC$cDLC$dNNC
050 00 $aQ172.5.C45$bO87 1993
082 00 $a003/.7$220
100 1 $aOtt, Edward.$0http://id.loc.gov/authorities/names/n82029693
245 10 $aChaos in dynamical systems /$cEdward Ott.
260 $aCambridge [England] ;$aNew York, NY, USA :$bCambridge University Press,$c1993.
263 $a9303
300 $axii, 385 pages :$billustrations ;$c26 cm
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
504 $aIncludes bibliographical references (p. 363-381) and index.
505 2 $a1. Introduction and overview. 1.1. Some history. 1.2. Examples of chaotic behavior. 1.3. Dynamical systems. 1.4. Attractors. 1.5. Sensitive dependence on initial conditions. 1.6. Delay coordinates -- 2. One-dimensional maps. 2.1. Piecewise linear one-dimensional maps. 2.2. The logistic map. 2.3. General discussion of smooth one-dimensional maps. 2.4. Examples of applications of one-dimensional maps to chaotic systems of higher dimensionality -- Appendix: Some elementary definitions and theorems concerning sets -- 3. Strange attractors and fractal dimension. 3.1. The box-counting dimension. 3.2. The generalized baker's map. 3.3. Measure and the spectrum of D[subscript d] dimensions. 3.4. Dimension spectrum for the generalized baker's map. 3.5. Character of the natural measure for the generalized baker's map. 3.6. The pointwise dimension. 3.7. Implications and determination of fractal dimension in experiments. 3.8. Embedding. 3.9. Fat fractals -- Appendix: Hausdorff dimension.
505 0 $a4. Dynamical properties of chaotic systems. 4.1. The horseshoe map and symbolic dynamics. 4.2. Linear stability of steady states and periodic orbits. 4.3. Stable and unstable manifolds. 4.4. Lyapunov exponents. 4.5. Entropies. 4.6. Controlling chaos -- Appendix: Gram-Schmidt orthogonalization -- 5. Nonattracting chaotic sets. 5.1. Fractal basin boundaries. 5.2. Final state sensitivity. 5.3. Structure of fractal basin boundaries. 5.4. Chaotic scattering. 5.5. The dynamics of chaotic scattering. 5.6. The dimensions of nonattracting chaotic sets and their stable and unstable manifolds -- Appendix: Derivation of Eqs. (5.3) -- 6. Quasiperiodicity. 6.1. Frequency spectrum and attractors. 6.2. The circle map. 6.3. N frequency quasiperiodicity with N > 2. 6.4. Strange nonchaotic attractors of quasiperiodically forced systems -- 7. Chaos in Hamiltonian systems. 7.1. Hamiltonian systems. 7.2. Perturbation of integrable systems.
505 0 $a7.3. Chaos and KAM tori in systems describable by two-dimensional Hamiltonian maps. 7.4. Higher-dimensional systems. 7.5. Strongly chaotic systems. 7.6. The succession of increasingly random systems -- 8. Chaotic transitions. 8.1. The period doubling cascade route to chaotic attractors. 8.2. The intermittency transition to a chaotic attractor. 8.3. Crises. 8.4. The Lorenz system: An example of the creation of a chaotic transient. 8.5. Basin boundary metamorphoses. 8.6. Bifurcations to chaotic scattering -- 9. Multifractals. 9.1. The singularity spectrum f(x). 9.2. The partition function formalism. 9.3. Lyapunov partition functions. 9.4. Distribution of finite time Lyapunov exponents. 9.5. Unstable periodic orbits and the natural measure. 9.6. Validity of the Lyapunov and periodic orbits partition functions for nonhyperbolic attractors -- 10. Quantum chaos. 10.1. The energy level spectra of chaotic, bounded, time-independent systems.
505 0 $a10.2. Wavefunctions for classically chaotic, bounded, time-independent systems. 10.3. Temporally periodic systems. 10.4. Quantum chaotic scattering.
650 0 $aChaotic behavior in systems.$0http://id.loc.gov/authorities/subjects/sh85022562
852 00 $bmat$hQ172.5.C45$iO87 1993
852 00 $bglg$hQ172.5.C45$iO87 1993
852 00 $bmat$hQ172.5.C45$iO87 1993
852 00 $boff,phy$hQ172.5.C45$iO87 1993