The Mathieu Differential Equation and Generalizations to Infinite Fractafolds

 

Introduction

Figures for the MDE on the Line

Figures for the Fractal MDE

Contact Info

ArXiV Link


Figures for the MDE on $SG_\infty$:

 

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Transition curves for version 1, 5 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 1, 5 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 1, 6 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 1, 6 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 2, 5 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 2, 5 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 2, 6 series, of single matrix corresponding to generation of birth $0$.
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Transition curves for version 2, 6 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).

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Transition curves for version 3, 5 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 3, 5 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 3, 6 series, of a single matrix corresponding to generation of birth $0$.
missing
Transition curves for version 3, 6 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 4, 5 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 4, 5 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Transition curves for version 4, 6 series, of a single matrix corresponding to generation of birth $0$.
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Transition curves for version 4, 6 series, of generation of birth 0 (red), -1 (blue), -2 (green), -3 (orange), -4 (black).
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Solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
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Solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=10000,11000,12000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=10000,11000,12000$.
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Solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
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Solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
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Solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with, with $\varepsilon=10000,11000,12000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with, with $\varepsilon=10000,11000,12000$.
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Solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
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Overlook of solutions on the first curve for choice 1, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
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Solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$
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Overlook of solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
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Solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=10000,11000,12000$.
missing
Overlook of solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=10000,11000,12000$.
missing
Solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 2, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$
missing
Solutions on the first curve for choice 2, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Overlook of solutions on the first curve for choice 2, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Solutions on the first curve for choice 2, initial eigenvalue $6$, initial eigenvalue $6$, with, with $\varepsilon=10000,11000,12000$.
missing
Overlook of solutions on the first curve for choice 2, initial eigenvalue $6$, initial eigenvalue $6$, with, with $\varepsilon=10000,11000,12000$.
missing
Solutions on the first curve for choice 2, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 2, initial eigenvalue $6$, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
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Solutions on the first curve for choice 3, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
missing
Overlook of solutions on the first curve for choice 3, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
missing
Solutions on the first curve for choice 3, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 3, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
missing
Solutions on the first curve for choice 3, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Overlook of solutions on the first curve for choice 3, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Solutions on the first curve for choice 3, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 3, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
missing
Solutions on the first curve for choice 4, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
missing
Overlook of solutions on the first curve for choice 4, initial eigenvalue $5$, with $\varepsilon=1000,2000,3000$.
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Solutions on the first curve for choice 4, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 4, initial eigenvalue $5$, with $\varepsilon=20000,25000,30000$.
missing
Solutions on the first curve for choice 4, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Overlook of solutions on the first curve for choice 4, initial eigenvalue $6$, with $\varepsilon=1000,2000,3000$.
missing
Solutions on the first curve for choice 4, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
missing
Overlook of solutions on the first curve for choice 4, initial eigenvalue $6$, with $\varepsilon=20000,25000,30000$.
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The position of peaks for version 1, 5 series.
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The position of peaks for version 1, 5 series.
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The position of peaks for version 1, 6 series.
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The position of peaks for version 1, 6 series.
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The position of peaks for version 2, 5 series.
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The position of peaks for version 2, 5 series.
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The position of peaks for version 2, 6 series.
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The position of peaks for version 2, 6 series.
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The position of peaks for version 3, 5 series.
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The position of peaks for version 3, 5 series.
missing
The position of peaks for version 3, 6 series.
missing
The position of peaks for version 3, 6 series.
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The position of peaks for version 4, 5 series.
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The position of peaks for version 4, 5 series.
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The position of peaks for version 4, 6 series.
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The position of peaks for version 4, 6 series.