Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map

Avrutin, Viktor, et al. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map ." ESAIM: Proceedings 36 (2012): 126-158. <http://eudml.org/doc/251237>.

@article{Avrutin2012,
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.},
author = {Avrutin, Viktor, Futter, Ben, Gardini, Laura, Schanz, Michael},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {piecewise-smooth maps; discontinuous flat top tent map; maps with a horizontal part; nested period incrementing; Milnor attractors; U-sequence},
language = {eng},
month = {8},
pages = {126-158},
publisher = {EDP Sciences},
title = { Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map },
url = {http://eudml.org/doc/251237},
volume = {36},
year = {2012},
}

TY - JOUR
AU - Avrutin, Viktor
AU - Futter, Ben
AU - Gardini, Laura
AU - Schanz, Michael
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 126
EP - 158
AB - 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.
LA - eng
KW - piecewise-smooth maps; discontinuous flat top tent map; maps with a horizontal part; nested period incrementing; Milnor attractors; U-sequence
UR - http://eudml.org/doc/251237
ER -