155 citations · 698 across the 55 of their papers we have counts for
7 papers · 1 filter
Incommensurate standard map
Leonardo Ermann, Dima L. Shepelyansky
We introduce and study the extension of the Chirikov standard map when the kick potential has two and three incommensurate spatial harmonics. This system is called the incommensura…
Symbolic walk in regular networks
L. Ermann, G. G. Carlo
We find that a symbolic walk (performed by a walker with memory given by a Bernoulli shift) is able to distinguish between the random or chaotic topology of a given network. We sho…
Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
Leonardo Ermann, Dima L. Shepelyansky
We study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain st…
Arnold cat map, Ulam method and time reversal
Leonardo Ermann, Dima L. Shepelyansky
We study the properties of the Arnold cap map on a torus with a several periodic sections using the Ulam method. This approach generates a Markov chain with the Ulam matrix approxi…
Ulam method and fractal Weyl law for Perron--Frobenius operators
Leonardo Ermann, Dima L. Shepelyansky
We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show that the spectrum is c…
A periodic orbit basis for the Quantum Baker Map
Leormardo Ermann, Marcos Saraceno
A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum versio…