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Exploring invariant sets and invariant measures
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997We propose a method to explore invariant measures of dynamical systems. The method is based on numerical tools which directly compute invariant sets using a subdivision technique, and invariant measures by a discretization of the Frobenius-Perron operator. Appropriate visualization tools help to analyze the numerical results and to understand important
Dellnitz, Michael +3 more
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1998
Abstract A measure is a generalization of what we mean by area in the plane and volume in three dimensions. A measure assigns a “size” to a set. Thus, for example, the measure of disjoint sets should be the sum of the measures of each. It turns out that there are some sets so “bad” that they cannot be assigned a measure in a natural way.
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Abstract A measure is a generalization of what we mean by area in the plane and volume in three dimensions. A measure assigns a “size” to a set. Thus, for example, the measure of disjoint sets should be the sum of the measures of each. It turns out that there are some sets so “bad” that they cannot be assigned a measure in a natural way.
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Measurement of color invariants
Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662), 2002This paper presents the measurement of object reflectance from color images. We exploit the Gaussian scale-space paradigm to define framework for the robust measurement of object reflectance from color images. Illumination and geometrical invariant properties are derived from a physical reflectance model based on the Kubelka-Munk theory.
Geusebroek, J.M. +2 more
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Invariant, relatively invariant, and quasi-invariant measures
1989In this section we discuss existence and uniqueness of invariant, relatively invariant and quasi-invariant measures on a space χ with an acting group G. In particular, the left and right invariant measures on G itself are considered, and several basic formulas relating these are derived. Various disintegration formulas are also presented.
Ole E. Barndorff-Nielsen +2 more
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2013
Bounded randomness of mass/energy exchange rates neither presuppose nor selects any specific time scale, thresholds of stability included. Nonetheless, the boundedness of the rates sets certain non-physical correlations among successive increments and thus justifies formation of “sub-walks” on the finest scale.
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Bounded randomness of mass/energy exchange rates neither presuppose nor selects any specific time scale, thresholds of stability included. Nonetheless, the boundedness of the rates sets certain non-physical correlations among successive increments and thus justifies formation of “sub-walks” on the finest scale.
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Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems
Journal of Dynamics and Differential Equations, 2021Bixiang Wang, Xiaohu Wang, Dingshi
exaly