000			04768nam a22004695i 4500
001			978-0-8176-4927-2
003			DE-He213
005			20251006084439.0
007			cr nn 008mamaa
008			100301s2009 xxu| s |||| 0|eng d
020			_a9780817649272
020			_a99780817649272
024	7		_a10.1007/978-0-8176-4927-2 _2doi
082	0	4	_a515.39 _223
082	0	4	_a515.48 _223
100	1		_aCollet, Pierre. _eauthor.
245	1	0	_aIterated Maps on the Interval as Dynamical Systems _h[electronic resource] / _cby Pierre Collet, Jean-Pierre Eckmann.
264		1	_aBoston : _bBirkhäuser Boston, _c2009.
300			_aX, 248p. 67 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aMotivation and Interpretation -- One-Parameter Families of Maps -- Typical Behavior for One Map -- Parameter Dependence -- Systematics of the Stable Periods -- On the Relative Frequency of Periodic and Aperiodic Behavior -- Scaling and Related Predictions -- Higher Dimensional Systems -- Properties of Individual Maps -- Unimodal Maps and Thier Itineraries -- The Calculus of Itineraries -- Itineraries and Orbits -- Negative Schwarzian Derivative -- Homtervals -- Topological Conjugacy -- Sensitive Dependence on Initial Conditions -- Ergodic Properties -- Properties of one-Parameter families of maps -- One-Parameter Families of Maps -- Abundance of Aperiodic Behavior -- Universal Scaling -- Multidimensional Maps.
520			_aIterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems . This book is a thorough and readable introduction to some aspects of the theory of one-dimensional dynamical systems...The kneading calculus of Milnor-Thurston receives its most accessible treatment to date in print...This is an important and beautiful exposition, both as an orientation for the reader unfamiliar with this theory and as a prelude to studying in greater depth some of the hard papers on the subject. -Mathematical Reviews (Review of the original hardcover edition) This book provides a good survey of recent developments in the study of the dynamics of smooth self-maps on the interval. It...deals with a subject whose literature often appears in physics journals. This literature suffers in general from a failure to distinguish between mathematical theorems and 'facts' determined empirically, usually by computer experiment. It is a difficult task to consider both of these types of information and carefully maintain the distinction (an absolute necessity from the point of view of a mathematician). The work under review seems to do a good job of this...On the whole this work is a good one meeting a need to survey recent results in this active and important area of mathematics. -Zentralblatt MATH (Review of the original hardcover edition)
650		0	_aMATHEMATICS.
650		0	_aDIFFERENTIABLE DYNAMICAL SYSTEMS.
650		0	_aMATHEMATICAL PHYSICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aDYNAMICAL SYSTEMS AND ERGODIC THEORY.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
700	1		_aEckmann, Jean-Pierre. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817649265
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4927-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59823 _d59823