# Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

Laura Gardini; Viktor Avrutin; Michael Schanz; Albert Granados; Iryna Sushko

ESAIM: Proceedings (2012)

- Volume: 36, page 106-120
- ISSN: 1270-900X

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topGardini, Laura, et al. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches ." ESAIM: Proceedings 36 (2012): 106-120. <http://eudml.org/doc/251250>.

@article{Gardini2012,

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.},

author = {Gardini, Laura, Avrutin, Viktor, Schanz, Michael, Granados, Albert, Sushko, Iryna},

editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},

journal = {ESAIM: Proceedings},

keywords = {piecewise smooth maps; border collision bifurcations; organizing centers},

language = {eng},

month = {8},

pages = {106-120},

publisher = {EDP Sciences},

title = { Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches },

url = {http://eudml.org/doc/251250},

volume = {36},

year = {2012},

}

TY - JOUR

AU - Gardini, Laura

AU - Avrutin, Viktor

AU - Schanz, Michael

AU - Granados, Albert

AU - Sushko, Iryna

AU - Fournier-Prunaret, D.

AU - Gardini, L.

AU - Reich, L.

TI - Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

JO - ESAIM: Proceedings

DA - 2012/8//

PB - EDP Sciences

VL - 36

SP - 106

EP - 120

AB - 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.

LA - eng

KW - piecewise smooth maps; border collision bifurcations; organizing centers

UR - http://eudml.org/doc/251250

ER -

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