Invariant Measures for the n-Dimensional Border Collision Normal Form
نویسندگان
چکیده
منابع مشابه
Invariant Measures for the n-Dimensional Border Collision Normal Form
The border collision normal form is a continuous piecewise affine map of R n with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence that the attractors have Haus-dorff (fractal) dimension n. If n = 2 the attractors have topological dimension two, i.e. they contain open sets, and...
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In this work we study some properties associated with the bordercollision bifurcations in a two-dimensional piecewise linear map in canonical form, related to the case in which a xed point of one of the linear maps has complex eigenvalues and undergoes a center bifurcation when its eigenvalues pass through the unit circle. This problem is faced in several applied piecewise smooth models, such ...
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The N -dimensional border collision normal form describes bifurcations of piecewise smooth systems. It is shown that there is an open set of parameters such that on one side of the bifurcation the map has a stable fixed point and on the other an attractor with Hausdorff dimension N . For generic parameters this attractor contains open sets and hence has topological dimension equal to N . PACS n...
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The deterministic border collision normal form describes the bifurcations of a discrete time dynamical system as a fixed point moves across the switching surface with changing parameter. If the position of the switching surface varies randomly, but within some bounded region, we give conditions which imply that the attractor close to the bifurcation point is the attractor of an Iterated Functio...
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Abstract. In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the plane of discontinuity. Earlier, Feigin had made a similar analysis for general n-dimensional piecewise smooth continuous maps. Proceeding along sim...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 2014
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127414501648