@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 = {Article in Journal},
   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 = {English},
   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 = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
   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=1}
}

@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 = {Article in Journal},
   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 = {English},
   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 = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
   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=1}
}