Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems   We investigate the connection between local and global dynamics of two
N-degree of freedom Hamiltonian systems with different origins describing
one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a
discretized version of the nonlinear Schrodinger equation related to
Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity
of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase
motion (OPM), which are known in closed form and whose linear stability can be
analyzed exactly. Our results verify that as the energy E increases for fixed
N, beyond the destabilization threshold of these orbits, all positive Lyapunov
exponents exhibit a transition between two power laws, occurring at the same
value of E. The destabilization energy E_c per particle goes to zero as N goes
to infinity following a simple power-law. However, using SALI, a very efficient
indicator we have recently introduced for distinguishing order from chaos, we
find that the two Hamiltonians have very different dynamics near their stable
SPOs: For example, in the case of the FPU system, as the energy increases for
fixed N, the islands of stability around the OPM decrease in size, the orbit
destabilizes through period-doubling bifurcation and its eigenvalues move
steadily away from -1, while for the BEC model the OPM has islands around it
which grow in size before it bifurcates through symmetry breaking, while its
real eigenvalues return to +1 at very high energies. Still, when calculating
Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov
exponents decrease following an exponential law and yield extensive
Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed
energy density E/N with E and N arbitrarily large.

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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph