Publikationen BV: Bibliographie 2012 BibTeX
@article {ART-2012-20,
author = {Viktor Avrutin and Ben Futter and Laura Gardini and Michael Schanz},
title = {{Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map}},
journal = {ESAIM: Proceedings},
publisher = {EDP Sciences},
volume = {36},
pages = {126--158},
type = {Artikel in Zeitschrift},
month = {April},
year = {2012},
doi = {10.1051/proc/201236011},
keywords = {piecewise-smooth maps; discontinuous flat top tent map; maps with a horizontal part; nested period incrementing; Milnor attractors; U-sequence},
language = {Englisch},
cr-category = {G.2 Discrete Mathematics},
ee = {ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/ART-2012-20/ART-2012-20.pdf},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we consider the discontinuous flat top tent map which represents
an example for discontinuous piecewise-smooth maps, whereby the system function
is constant on some interval. Such maps show several characteristics caused by
this constant value which are still insufficiently investigated. In this work
we demonstrate that in the discontinuous flat top tent map every unstable
periodic orbit may become a Milnor attractor. Moreover, it turns out that there
exists a strong connection between stable and unstable orbits and that the
appearance of a single unstable orbit may cause an infinite number of stable
orbits to appear. Based on this connection we provide a more precise
explanation of the recently discovered self-similar bifurcation scenario
occurring in the discontinuous flat top tent map denoted as the nested period
incrementing scenario.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2012-20&engl=0}
}
@article {ART-2012-05,
author = {Ben Futter and Viktor Avrutin and Michael Schanz},
title = {{The discontinuous flat top tent map and the nested period incrementing bifurcation structure}},
journal = {Chaos, Solitons \& Fractals},
publisher = {Elsevier},
volume = {45},
number = {4},
pages = {465--482},
type = {Artikel in Zeitschrift},
month = {April},
year = {2012},
doi = {10.1016/j.chaos.2012.01.009},
issn = {0960-0779},
keywords = {discontinuous flat top tent map; nested period incrementing; symbolic dynamics; U-sequence; discontinuous maps},
language = {Englisch},
cr-category = {G.2.0 Discrete Mathematics General,
J.2 Physical Sciences and Engineering},
ee = {ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/ART-2012-05/ART-2012-05.pdf,
http://dx.doi.org/10.1016/j.chaos.2012.01.009},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we report the recently discovered nested period incrementing
bifurcation scenario. The investigated piecewise linear map is defined on three
partitions of the unit interval, constant in the middle partition and therefore
displays a rich variety of superstable orbits. These orbits are arranged
according to an infinite binary tree of the corresponding symbolic sequences,
which can be generated by a simple set of rules. The system also allows for
straightforward computation of the respective regions of existence. One of the
most striking results of our investigations is that the famous U-sequence is
inevitably embedded in the nested period incrementing scenario.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2012-05&engl=0}
}
