| 000 | 06027nam a2200805 i 4500 | ||
|---|---|---|---|
| 001 | 6813366 | ||
| 003 | IEEE | ||
| 005 | 20200413152903.0 | ||
| 006 | m eo d | ||
| 007 | cr cn |||m|||a | ||
| 008 | 110925s2011 caua foab 001 0 eng d | ||
| 020 | _a9781598299151 (electronic bk.) | ||
| 020 | _z9781598299144 (pbk.) | ||
| 024 | 7 |
_a10.2200/S00373ED1V01Y201107MAS011 _2doi |
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| 035 | _a(CaBNVSL)gtp00549567 | ||
| 035 | _a(OCoLC)752659371 | ||
| 040 |
_aCaBNVSL _cCaBNVSL _dCaBNVSL |
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| 050 | 4 |
_aQ172.5.C45 _bC443 2011 |
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| 082 | 0 | 4 |
_a500.201185 _222 |
| 100 | 1 |
_aChen, Goong, _d1950- |
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| 245 | 1 | 0 |
_aChaotic maps _h[electronic resource] : _bdynamics, fractals, and rapid fluctuations / _cGoong Chen and Yu Huang. |
| 260 |
_aSan Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool, _cc2011. |
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| 300 |
_a1 electronic text (xiii, 227 p.) : _bill., digital file. |
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| 490 | 1 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 11 |
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| 538 | _aMode of access: World Wide Web. | ||
| 538 | _aSystem requirements: Adobe Acrobat Reader. | ||
| 500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
| 500 | _aSeries from website. | ||
| 504 | _aIncludes bibliographical references (p. 217-222) and index. | ||
| 505 | 0 | _a1. Simple interval maps and their iterations -- 1.1 Introduction -- 1.2 The inverse and implicit function theorems -- 1.3 Visualizing from the graphics of iterations of the quadratic map -- Notes for chapter 1 -- | |
| 505 | 8 | _a2. Total variations of iterates of maps -- 2.1 The use of total variations as a measure of chaos -- Notes for chapter 2 -- | |
| 505 | 8 | _a3. Ordering among periods: the Sharkovski theorem -- Notes for chapter 3 -- | |
| 505 | 8 | _a4. Bifurcation theorems for maps -- 4.1 The period-doubling bifurcation theorem -- 4.2 Saddle-node bifurcations -- 4.3 The pitchfork bifurcation -- 4.4 Hopf bifurcation -- Notes for chapter 4 -- | |
| 505 | 8 | _a5. Homoclinicity. Lyapunoff exponents -- 5.1 Homoclinic orbits -- 5.2 Lyapunoff exponents -- Notes for chapter 5 -- | |
| 505 | 8 | _a6. Symbolic dynamics, conjugacy and shift invariant sets -- 6.1 The itinerary of an orbit -- 6.2 Properties of the shift map -- 6.3 Symbolic dynamical systems -- 6.4 The dynamics of [Sigma ...] and chaos -- 6.5 Topological conjugacy and semiconjugacy -- 6.6 Shift invariant sets -- 6.7 Construction of shift invariant sets -- 6.8 Snap-back repeller as a shift invariant set -- Notes for chapter 6 -- | |
| 505 | 8 | _a7. The Smale horseshoe -- 7.1 The standard Smale horseshoe -- 7.2 The general horseshoe -- Notes for chapter 7 -- | |
| 505 | 8 | _a8. Fractals -- 8.1 Examples of fractals -- 8.2 Hausdorff dimension and the Hausdorff measure -- 8.3 Iterated function systems (IFS) -- Notes for chapter 8 -- | |
| 505 | 8 | _a9. Rapid fluctuations of chaotic maps on RN -- 9.1 Total variation for vector-value maps -- 9.2 Rapid fluctuations of maps on RN -- 9.3 Rapid fluctuations of systems with quasi-shift invariant sets -- 9.4 Rapid fluctuations of systems containing topological horseshoes -- 9.5 Examples of applications of rapid fluctuations -- Notes for chapter 9 -- | |
| 505 | 8 | _a10. Infinite-dimensional systems induced by continuous-time difference equations -- 10.1 I3DS -- 10.2 Rates of growth of total variations of iterates -- 10.3 Properties of the set B(f ) -- 10.4 Properties of the set U(f ) -- 10.5 Properties of the set E(f ) -- Notes for chapter 10 -- | |
| 505 | 8 | _aA. Introduction to continuous-time dynamical systems -- The local behavior of 2-dimensional nonlinear systems -- Index for two-dimensional systems -- The Poincare map for a periodic orbit in RN -- B. Chaotic vibration of the wave equation due to energy pumping and van der Pol boundary conditions -- The mathematical model and motivations -- Chaotic vibration of the wave equation -- Authors' biographies -- Index. | |
| 506 | 1 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | |
| 510 | 0 | _aCompendex | |
| 510 | 0 | _aINSPEC | |
| 510 | 0 | _aGoogle scholar | |
| 510 | 0 | _aGoogle book search | |
| 520 | 3 | _aThis book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years.Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. | |
| 530 | _aAlso available in print. | ||
| 588 | _aTitle from PDF t.p. (viewed on September 25, 2011). | ||
| 650 | 0 |
_aChaotic behavior in systems _xMathematics. |
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| 650 | 0 | _aMappings (Mathematics) | |
| 653 | _achaos | ||
| 653 | _ainterval maps | ||
| 653 | _aperiodicity | ||
| 653 | _asensitive dependence | ||
| 653 | _astability | ||
| 653 | _aSharkovski's theorem | ||
| 653 | _abifurcations | ||
| 653 | _ahomoclinicity | ||
| 653 | _asymbolic dynamics | ||
| 653 | _asmale horseshoe | ||
| 653 | _atotal variations | ||
| 653 | _arapid fluctuations | ||
| 653 | _afractals | ||
| 653 | _awave equation | ||
| 700 | 1 |
_aHuang, Yu, _d1963- |
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| 776 | 0 | 8 |
_iPrint version: _z9781598299144 |
| 830 | 0 | _aSynthesis digital library of engineering and computer science. | |
| 830 | 0 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 11. |
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| 856 | 4 | 2 |
_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=6813366 |
| 999 |
_c561871 _d561871 |
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