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A Linear Spline Maximum Entropy Method for Frobenius-Perron Operators of Multi-dimensional Transformations

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Abstract

A piecewise linear spline maximum entropy optimization method is described for the approximation of fixed densities of the Frobenius-Perron operator associated with higher-dimensional transformations. Convergence in \(L^1\)-norm is proved and several examples with results are given.

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Acknowledgements

The authors are grateful to anonymous reviewers for their valuable comments which improved the presentation of the paper. This research is funded by NSERC DG grant 2017-05321 of Md Shafiqul Islam at the University of Prince Edward Island, PE, Canada. Adam Smith is an undergraduate student in the School of Mathematical and Computational Sciences at the University of Prince Edward island and he grateful to NSERC for financial support for his USRA fund at the University of Prince Edward Island. Adam Smith is also grateful to his NSERC USRA supervisor Prof. Md Shafiqul Islam and the School of Mathematical and Computational Science at the University of Prince Edward Island for the hospitality during the tenure of his undergraduate NSERC USRA.

Funding

This research is partially supported by NSERC DG grant of Md Shafiqul Islam at the University of Prince Edward Island, PE, Canada. Adam Smith is grateful to NSERC for financial support for his USRA fund at the University of Prince Edward Island.

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  1. School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Ave, Charlottetown, PE, C1A 4P3, Canada

    Md Shafiqul Islam & Adam Smith

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  1. Md Shafiqul Islam
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Correspondence to Md Shafiqul Islam.

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Islam, M.S., Smith, A. A Linear Spline Maximum Entropy Method for Frobenius-Perron Operators of Multi-dimensional Transformations. Int. J. Appl. Comput. Math 8, 180 (2022). https://doi.org/10.1007/s40819-022-01386-2

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