Tag Archives: mathematics

Counting primes, arithmetic functions, Ramanujan and the like

We originally wished to have a tail-piece for our previous note that would describe more precisely the relationship between the Möbius function and the distribution of prime numbers. However, since that would have needed a bit of a detour in … Continue reading

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Our auto-discovery of the Möbius and Mertens sequences

Recently, we were explaining to our friend the Möbius and the Mertens functions and their relationship to the prime number distribution. We also heard with some wonder from a physicist of a theoretical model where multiparticle states behave as bosons … Continue reading

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The incredible beauty of certain Hamiltonian mappings

In our teens we studied Hamiltonian functions a little bit as part of our attempt to understand classical and quantum physics. A byproduct of it was a superficial interest in the geometry of some of the mappings arising from such … Continue reading

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The Satija-Ketoja system

Satija and Ketoja discovered an interesting dynamical system in course of the study of the Schrödinger equation for one electron in a two dimensional periodic lattice on a uniform magnetic field. While this equation and its variants have several uses … Continue reading

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Some simple maps specifying strange attractors

This note may be read a continuation of: Some reminiscences of our study of chaotic maps-2 While the story of the chaotic 2D attractors began with the simple-looking maps of Henon and Lozi, by the early 1990s the high-point was … Continue reading

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The Meru and Nārāyaṇa’s cows: Words and fractals

The fractals described herein are based on and inspired by the work of the mathematicians Rauzy, Mendes-France, Monnerot and Knuth. Some their works, especially the first of them, are dense with formalism. Here we present in simple terms the means … Continue reading

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Hofstadter and Nārāyaṇa: connections across space and time

The scientist-philosopher Douglas Hofstadter presents an interesting single-seeded sequence H in his book ‘Gödel, Escher, Bach: An Eternal Golden Braid’. It is generated by the recurrence relation, where …(1) Working it out one can see that it takes the form: … Continue reading

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