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001 978-3-319-47837-1
003 DE-He213
005 20210118154250.0
007 cr nn 008mamaa
008 161215s2017 gw | s |||| 0|eng d
020 _a9783319478371
_9978-3-319-47837-1
024 7 _a10.1007/978-3-319-47837-1
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.1
_223
100 1 _aElaskar, Sergio.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNew Advances on Chaotic Intermittency and its Applications
_h[electronic resource] /
_cby Sergio Elaskar, Ezequiel del Río.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXVIII, 197 p. 99 illus., 62 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aChapter 1: Introduction to chaotic intermittency -- Chapter 2: Other types of intermittency and some recent advances in the study of chaotic intermittency -- Chapter 3: Some applications of the chaotic Intermittency -- Chapter 4: Classical theory about noise effects in chaotic intermittency -- Chapter 5: New formulation of the chaotic intermittency -- Chapter 6: New formulation of the noise effects in chaotic intermittency -- Chapter 7: Application of the new formulation to pathological cases -- Chapter 8: Application to dynamical systems. An example with discontinuous RPD: the derivative nonlinear Schrodinger equation -- Chapter 9: Evaluation of the intermittency statistical properties using the Perron-Frobenius operator.
520 _aOne of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data. As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittency type, is now a function depending on the whole map, not just on the local map. Also, a new analytical approach to obtain the RPD from the mathematical expression of the map is presented. In this way all cases of non standard intermittencies are included in the same frame work. This methodology is extended to evaluate the noisy reinjection probability density function (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. This is an important difference with respect to the classical approach based on the Fokker-Plank equation or Renormalization Group theory, where the noise effect was usually considered just on the local Poincaré map. Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. Along the book examples of applications are described, which have shown very good agreement with numerical computations. .
650 0 _aMechanics.
650 0 _aMechanics, Applied.
650 0 _aFluids.
650 0 _aMathematical physics.
650 0 _aComputational complexity.
650 0 _aElectrical engineering.
650 0 _aNeurosciences.
650 1 4 _aTheoretical and Applied Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/T15001
650 2 4 _aFluid- and Aerodynamics.
_0http://scigraph.springernature.com/things/product-market-codes/P21026
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aComplexity.
_0http://scigraph.springernature.com/things/product-market-codes/T11022
650 2 4 _aElectrical Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/T24000
650 2 4 _aNeurosciences.
_0http://scigraph.springernature.com/things/product-market-codes/B18006
700 1 _adel Río, Ezequiel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319478364
776 0 8 _iPrinted edition:
_z9783319478388
776 0 8 _iPrinted edition:
_z9783319838366
856 4 0 _uhttps://doi.org/10.1007/978-3-319-47837-1
912 _aZDB-2-ENG
999 _c453803
_d453803
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/