Speaker
Description
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{\bf\Large READING MULTIPLICITY IN UNFOLDINGS
FROM $\varepsilon$-NEIGHBORHOODS OF ORBITS
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{\sc\large Renato Huzak}
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{\em Hasselt University, Belgium \
E-mail: renato.huzak@uhasselt.be}
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{\sc\large Pavao Marde\v si\' c}
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{\em Universit\' e de Bourgogne, France\
E-mail: pavao.mardesic@u-bourgogne.fr}
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{\sc\large Maja Resman}
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{\em University of Zagreb Faculty of Science\
E-mail: mresman@math.hr}
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{\sc\large Vesna \v Zupanovi\' c}
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{\em University of Zagreb Faculty of Electrical Engineering and Computing\
E-mail: vesna.zupanovic@fer.hr}
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In \cite{Reference2} we study the relationship between the multiplicity of
a fixed point of a function $g$, and the dependence on $\varepsilon$ of the length
of $\varepsilon$-neighborhood of any discrete orbit of $g$, tending to the fixed point. We study
the space of functions having a development in a Chebyshev scale
and use multiplicity with respect to this space of functions.
We introduce critical Minkowski order, the notion recovering the relationship between the multiplicity
of fixed points and the dependence on $\varepsilon$ of the length of $\varepsilon$-neighborhood
of orbits. In \cite{Reference1} we introduce a parameter in the generator function $g$. Using the new notion of continuous $\varepsilon$-neighborhood of a discrete orbit we study saddle-node, transcritical and pitchfork bifurcation. We obtain the asymptotic expansion of the length of the continuous $\varepsilon$-neighborhood of a discrete orbit.
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\bibitem{Reference1} R. Huzak, P. Marde\v si\' c, M. Resman, V.
\v Zupanovi\' c, {\em Reading multiplicity in unfoldings from $\varepsilon$-neighborhoods of orbits}, preprint
\bibitem{Reference2} P. Marde\v si\' c, M. Resman, V. \v Zupanovi\' c, {\em Multiplicity of fixed points and $\varepsilon-$neighborhoods of orbits}, J. Differ. Equations 253 (2012), no. 8, 2493-2514
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