000 03985nam a22005295i 4500
001 978-1-4614-1891-7
003 DE-He213
005 20140220083244.0
007 cr nn 008mamaa
008 111117s2012 xxu| s |||| 0|eng d
020 _a9781461418917
_9978-1-4614-1891-7
024 7 _a10.1007/978-1-4614-1891-7
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aKunze, Herb.
_eauthor.
245 1 0 _aFractal-Based Methods in Analysis
_h[electronic resource] /
_cby Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay.
264 1 _aBoston, MA :
_bSpringer US,
_c2012.
300 _aXVI, 408 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aWhat do we mean by “Fractal-Based Analysis" -- Basic IFS -- IFS on Spaces of Functions -- IFS, Multifunctions, and Measure-Valued Functions. -IFS on Spaces of Measures.-The Chaos Game.-Inverse Problems and Fractal-Based Methods.-Further Developments and Extensions -- References -- Index.
520 _aThe idea of modeling the behavior of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems.   "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters.  For each topic the theoretical framework is carefully explained using examples and applications.   The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises.  This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences.   Herb Kunze is a Professor in the Department of Mathematics and Statistics, University of Guelph.  Davide La Torre is an Associate Professor in the Department of Economics, Business and Statistics, University of Milan.   Franklin Mendivil is a Professor in the Department of Mathematics and Statistics, Acadia University. Edward R. Vrscay is a Professor in the Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo.  A major focus of their research is fractals and their applications.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential Equations.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aApproximations and Expansions.
650 2 4 _aMathematical Modeling and Industrial Mathematics.
650 2 4 _aOrdinary Differential Equations.
700 1 _aLa Torre, Davide.
_eauthor.
700 1 _aMendivil, Franklin.
_eauthor.
700 1 _aVrscay, Edward R.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461418900
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-1891-7
912 _aZDB-2-SMA
999 _c101152
_d101152