Bifurcations of invariant measures in discrete-time parameter dependent cocycles

Anastasia Maltseva; Volker Reitmann

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 2, page 205-213
  • ISSN: 0862-7959

Abstract

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We consider parameter-dependent cocycles generated by nonautonomous difference equations. One of them is a discrete-time cardiac conduction model. For this system with a control variable a cocycle formulation is presented. We state a theorem about upper Hausdorff dimension estimates for cocycle attractors which includes some regulating function. We also consider the existence of invariant measures for cocycle systems using some elements of Perron-Frobenius theory and discuss the bifurcation of parameter-dependent measures.

How to cite

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Maltseva, Anastasia, and Reitmann, Volker. "Bifurcations of invariant measures in discrete-time parameter dependent cocycles." Mathematica Bohemica 140.2 (2015): 205-213. <http://eudml.org/doc/271641>.

@article{Maltseva2015,
abstract = {We consider parameter-dependent cocycles generated by nonautonomous difference equations. One of them is a discrete-time cardiac conduction model. For this system with a control variable a cocycle formulation is presented. We state a theorem about upper Hausdorff dimension estimates for cocycle attractors which includes some regulating function. We also consider the existence of invariant measures for cocycle systems using some elements of Perron-Frobenius theory and discuss the bifurcation of parameter-dependent measures.},
author = {Maltseva, Anastasia, Reitmann, Volker},
journal = {Mathematica Bohemica},
keywords = {discrete-time parameter-dependent cocycles; Hausdorff dimension estimate; invariant measure},
language = {eng},
number = {2},
pages = {205-213},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcations of invariant measures in discrete-time parameter dependent cocycles},
url = {http://eudml.org/doc/271641},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Maltseva, Anastasia
AU - Reitmann, Volker
TI - Bifurcations of invariant measures in discrete-time parameter dependent cocycles
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 2
SP - 205
EP - 213
AB - We consider parameter-dependent cocycles generated by nonautonomous difference equations. One of them is a discrete-time cardiac conduction model. For this system with a control variable a cocycle formulation is presented. We state a theorem about upper Hausdorff dimension estimates for cocycle attractors which includes some regulating function. We also consider the existence of invariant measures for cocycle systems using some elements of Perron-Frobenius theory and discuss the bifurcation of parameter-dependent measures.
LA - eng
KW - discrete-time parameter-dependent cocycles; Hausdorff dimension estimate; invariant measure
UR - http://eudml.org/doc/271641
ER -

References

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  8. Maltseva, A., Reitmann, V., 10.1134/S0012266114130035, Differ. Equ. 50 (2014), 1718-1732. (2014) Zbl1317.39008MR3372683DOI10.1134/S0012266114130035
  9. Reitmann, V., Dynamical Systems, Attractors and Estimates of Their Dimension, Saint Petersburg State University Press Saint Petersburg (2013), Russian. (2013) 
  10. Reitmann, V., Slepukhin, A. S., 10.3103/S1063454111040091, Vestn. St. Petersbg. Univ., Math. 44 (2011), 292-300 translation from Vestn. St.-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2011 (2011), 61-70. (2011) Zbl1303.37009MR2918529DOI10.3103/S1063454111040091
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