Abstract
This paper studies the asymptotic behavior of the eigenvalue counting function of the Laplacian on some weakly self-similar fractals called Hanoi attractors. A resistance form is constructed and equipped with a suitable measure in order to obtain a Dirichlet form and its associated Laplacian. Hereby, the classical construction for p.c.f. self-similar fractals has to be modified by combining discrete and quantum graph methods.
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Weyl asymptotics for Hanoi attractors
- Reconstruction of graded groupoids from graded Steinberg algebras
- Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method
- Mutations of simple-minded systems in Calabi–Yau categories generated by a spherical object
- Some homological properties of category 𝒪. IV
- Subgroups of direct products closely approximated by direct sums
- Takahasi semigroups
- Integration of controlled rough paths via fractional calculus
- Qualitative properties of positive solutions of quasilinear equations with Hardy terms
- Fourth power moment of coefficients of automorphic L-functions for GL(m)
- Reversible homogeneous Finsler metrics with positive flag curvature
Articles in the same Issue
- Frontmatter
- Weyl asymptotics for Hanoi attractors
- Reconstruction of graded groupoids from graded Steinberg algebras
- Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method
- Mutations of simple-minded systems in Calabi–Yau categories generated by a spherical object
- Some homological properties of category 𝒪. IV
- Subgroups of direct products closely approximated by direct sums
- Takahasi semigroups
- Integration of controlled rough paths via fractional calculus
- Qualitative properties of positive solutions of quasilinear equations with Hardy terms
- Fourth power moment of coefficients of automorphic L-functions for GL(m)
- Reversible homogeneous Finsler metrics with positive flag curvature