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A route to computational chaos revisited: noninvertibility and the breakup of an invariant circle
, 2003
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Shadowing and inverse shadowing in setvalued dynamical systems. Hyperbolic case
"... 2007 We introduce a new hyperbolicity condition for setvalued dynamical systems and show that this condition implies the shadowing and inverse shadowing properties. ..."
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2007 We introduce a new hyperbolicity condition for setvalued dynamical systems and show that this condition implies the shadowing and inverse shadowing properties.
Shadowing and the viability kernel algorithm
 Appl. Math. Optim
"... The aim of this paper is to derive estimates for the accuracy of the viability algorithm for systems which have shadowing properties. Recently developped shadowing results are applied in order to prove that the algorithm is linearly convergent for a certain class of right hand sides. Key words. viab ..."
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The aim of this paper is to derive estimates for the accuracy of the viability algorithm for systems which have shadowing properties. Recently developped shadowing results are applied in order to prove that the algorithm is linearly convergent for a certain class of right hand sides. Key words. viability kernel algorithm, shadowing AMS(MOS) subject classifications. 34A60, 37C50
DYNAMICS OF NONINVERTIBILITY IN DELAY EQUATIONS
, 2005
"... Models with a time delay often occur, since there is a naturally occurring delay in the transmission of information. A model with a delay can be noninvertible, which in turn leads to qualitative differences between the dynamical properties of a delay equation and the familiar case of an ordinary di ..."
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Models with a time delay often occur, since there is a naturally occurring delay in the transmission of information. A model with a delay can be noninvertible, which in turn leads to qualitative differences between the dynamical properties of a delay equation and the familiar case of an ordinary differential equation. We give specific conditions for the existence of noninvertible solutions in delay equations, and describe the consequences of noninvertibility.
A General Approach to Hyperbolicity for SetValued Maps
, 2009
"... We introduce a general notion of hyperbolicity for setvalued dynamical systems and discuss it in the framework of polytopevalued maps. ..."
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We introduce a general notion of hyperbolicity for setvalued dynamical systems and discuss it in the framework of polytopevalued maps.