Renewal Theorems and Their Application in Fractal Geometry

[1]  M. Kesseböhmer,et al.  Fractal curvature measures and Minkowski content for self-conformal subsets of the real line , 2012 .

[2]  Erhan Cinlar,et al.  Markov Renewal Theory: A Survey , 1973 .

[3]  Fractal curvatures and Minkowski content of self-conformal sets , 2012, 1211.3421.

[4]  Fractal curvature measures of self-similar sets , 2010, 1007.0696.

[5]  Marc Kessebohmer,et al.  Minkowski measurability of infinite conformal graph directed systems and application to Apollonian packings , 2017, 1702.02854.

[6]  Erin P. J. Pearse,et al.  Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable , 2015, 1501.03764.

[7]  E. Çinlar.  Exceptional Paper---Markov Renewal Theory: A Survey , 1975 .

[8]  Mariusz Urbański,et al.  Dimensions and Measures in Infinite Iterated Function Systems , 1996 .

[9]  Paul Erdös,et al.  A property of power series with positive coefficients , 1949 .

[10]  M. Zähle,et al.  Curvature-direction measures of self-similar sets , 2011, 1111.4457.

[11]  On the Minkowski Measurability of Self-Similar Fractals in R^d , 2010, 1006.5883.

[12]  M. Lapidus,et al.  Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions , 2005 .

[13]  Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets , 2014, 1403.5201.

[14]  Kenneth Falconer.  On the Minkowski measurability of fractals , 1995 .

[15]  M. Lapidus,et al.  Fractal Geometry and Number Theory , 1999 .

[16]  Michel L. Lapidus,et al.  The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums , 1993 .

[17]  K. Falconer.  Techniques in fractal geometry , 1997 .

[18]  Marc Kessebohmer,et al.  A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory , 2016, 1604.08252.

[19]  Michel L. Lapidus,et al.  Complex Dimensions and Zeta Functions: Geometry and spectra of fractal strings , 2012 .

[20]  D. Blackwell.  Extension of a renewal theorem , 1953 .

[21]  S. Winter,et al.  Lattice self-similar sets on the real line are not Minkowski measurable , 2018, Ergodic Theory and Dynamical Systems.

[22]  Hui Rao,et al.  On the open set condition for self-similar fractals , 2005 .

[23]  M. Mirzakhani,et al.  Introduction to Ergodic theory , 2010 .

[24]  B. Mandelbrot.  Measures of Fractal Lacunarity: Minkowski Content and Alternatives , 1995 .

[25]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[26]  S. Lalley.  Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits , 1989 .

[27]  Erin P. J. Pearse,et al.  Minkowski Measurability Results for Self-Similar Tilings and Fractals with Monophase Generators , 2011, 1104.1641.

[28]  P. Walters.  Convergence of the Ruelle operator for a function satisfying Bowen’s condition , 2000 .

[29]  M. Zähle,et al.  Curvature Measures of Singular Sets , 2020, Springer Monographs in Mathematics.

[30]  Marc Kessebohmer,et al.  Minkowski content and fractal Euler characteristic for conformal graph directed systems , 2012, 1211.7333.

[31]  S. Kombrink.  Renewal theorems for processes with dependent interarrival times , 2015, Advances in Applied Probability.

[32]  David Blackwell,et al.  A renewal theorem , 1948 .

[33]  D. Gatzouras,et al.  Lacunarity of self-similar and stochastically self-similar sets , 1999 .

[34]  Michel L. Lapidus,et al.  Fractal Geometry, Complex Dimensions and Zeta Functions , 2006 .

[35]  Mariusz Urbański,et al.  Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets , 2003 .