@inproceedings{3e4e425c56fb4d9da59fc22d827601a9,
title = "Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches",
abstract = "This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.",
keywords = "Piecewise smooth maps, Border collision bifurcations, Organizing centers",
author = "Laura Gardini and Viktor Avrutin and {Michael Schanz}, Michael and Albert Granados and Iryna Sushko",
year = "2012",
doi = "10.1051/proc/201236009",
language = "English",
series = "ESAIM: Proceedings and Surveys",
publisher = "EDP Sciences",
number = "April",
pages = "106--120",
booktitle = "ESAIM: Proceedings",
address = "France",
note = "European Conference on Iteration Theory (ECIT 2010), ECIT ; Conference date: 12-09-2010 Through 17-09-2010",
}