000			03199pam a2200325 a 4500
001			3051821
003			CUTN
005			20231016140421.0
008			960321s1996 nyua b 001 0 eng
010			_a 96014777
020			_a9780387947808
040			_aDLC _cDLC _dDLC
050	0	0	_aQA614.8 _b.H65 1996
082	0	0	_a514.74 _220 _bHOL
100	1		_aHolmgren, Richard A.
245	1	2	_aA first course in discrete dynamical systems / _cRichard A. Holmgren.
250			_a2nd ed.
260			_aNew York : _bSpringer, _cc1996.
300			_axv, 223 p. : _bill. ; _c24 cm.
490	0		_aUniversitext
504			_aIncludes bibliographical references (p. [215]-220) and index.
505			_aIntroduction Richard A. Holmgren Pages 1-8 A Quick Look at Functions Richard A. Holmgren Pages 9-20 The Topology of the Real Numbers Richard A. Holmgren Pages 21-29 Periodic Points and Stable Sets Richard A. Holmgren Pages 31-39 Sarkovskii’s Theorem Richard A. Holmgren Pages 41-46 Differentiability and Its Implications Richard A. Holmgren Pages 47-57 Parametrized Families of Functions and Bifurcations Richard A. Holmgren Pages 59-67 The Logistic Function Part I: Cantor Sets and Chaos Richard A. Holmgren Pages 69-86 The Logistic Function Part II: Topological Conjugacy Richard A. Holmgren Pages 87-93 The Logistic Function Part III: A Period-Doubling Cascade Richard A. Holmgren Pages 95-108 The Logistic Function Part IV: Symbolic Dynamics Richard A. Holmgren Pages 109-126 Newton’s Method Richard A. Holmgren Pages 127-151 Numerical Solutions of Differential Equations Richard A. Holmgren Pages 153-165 The Dynamics of Complex Functions Richard A. Holmgren Pages 167-192 The Quadratic Family and the Mandelbrot Set Richard A. Holmgren Pages 193-202 Back Matter Pages 203-224
520			_aDiscrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix.
650		0	_aDifferentiable dynamical systems.
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/enhancements/fy0817/96014777-d.html
856	4	1	_3Table of contents only _uhttp://www.loc.gov/catdir/enhancements/fy0817/96014777-t.html
906			_a7 _bcbc _corignew _d1 _eocip _f19 _gy-gencatlg
942			_2ddc _cPROJECT
999			_c39904 _d39904