Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / David Carfi [and three others], editors.

Format:

Book

Conference/Event

Contributor:

Carfi, David, 1971- editor.

Conference Name:

PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 : Messina, Italy)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 600

Contemporary mathematics, 1098-3627 ; 600 0271-4132

Language:

English

Subjects (All):

Fractals--Congresses.

Fractals.

Physical Description:

1 online resource (410 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2013.

Language Note:

English

Summary:

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Contents:

Preface

Separation Conditions for Iterated Function Systems with Overlaps

1 Introduction

2 Preliminaries

3 The finite type condition

4 More on the finite type condition

5 Generalized finite type condition

6 Weak separation condition

References

-point Configurations of Discrete Self-Similar Sets

2 Lower bounds for -point configurations of compatible fractals

3 Determinant fractal zeta functions

Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator

2 Generalized Fractal Strings and Their Complex Dimensions

3 The Spectral Operator and the Infinitesimal Shifts

4 Inverse and Direct Spectral Problems for Fractal Strings

5 Quasi-Invertibility and Almost Invertibility of the Spectral Operator

6 Spectral Reformulations of the Riemann Hypothesis and of Almost RH

7 Concluding Comments

8 Appendix A: Riemann's Explicit Formula

9 Appendix B: The Momentum Operator and Normality of

Analysis and Geometry of the Measurable Riemannian Structure on the SierpiÅski Gasket

2 SierpiÅski gasket and its standard Dirichlet form

3 Measurable Riemannian structure on the SierpiÅski gasket

4 Geometry under the measurable Riemannian structure

5 Short time asymptotics of the heat kernels

6 Ahlfors regularity and singularity of Hausdorff measure

7 Weyl's Laplacian eigenvalue asymptotics cont.

Notes:

"PISRS 2011, First International Conference : Analysis, Fractal Geometry, Dynamical Systems and Economics, November 8-12, 2011, Messina, Sicily, Italy."

"AMS Special Session, in memory of Benoit Mandelbrot : Fractal Geometry in Pure and Applied Mathematics, January 4-7, 2012, Boston, Massachusetts."

"AMS Special Session : Geometry and Analysis on Fractal Spaces, March 3-4, 2012, Honolulu, Hawaii."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1082-6