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Spectra of Perron–Frobenius operator and new construction of two dimensional low discrepancy sequences

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  • Mori Makoto

    (Department of Mathematics, College of Humanities and Sciences, Nihon University, Japan. Email: mori@math.chs.nihon-u.ac.jp)

Abstract

For high dimensional transformations, the essential spectral radius of the Perron–Frobenius operator restricted to some natural space is generally smaller than the reciprocals of the radius of convergence of the dynamical zeta function. We will construct transformations whose essential spectral radius coincide with the reciprocal of the radius of convergence of the dynamical zeta functions, and construct new type of 2 dimensional low discrepancy sequences.

Suggested Citation

  • Mori Makoto, 2008. "Spectra of Perron–Frobenius operator and new construction of two dimensional low discrepancy sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 14(1), pages 53-74, January.
    • Handle: RePEc:bpj:mcmeap:v:14:y:2008:i:1:p:53-74:n:3
    DOI: 10.1515/MCMA.2008.003
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    References listed on IDEAS

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    1. Mori Makoto, 2002. "Construction of two dimensional low discrepancy sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 159-170, December.
    2. Mori Makoto, 1999. "Discrepancy of sequences generated by piecewise monotone maps," Monte Carlo Methods and Applications, De Gruyter, vol. 5(1), pages 55-68, December.
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