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Data-Driven Stabilization of Periodic Orbits
IEEE Access, 2021 Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded within any chaotic
Jason J. Bramburger +2 more
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On the noise-induced passage through an unstable periodic orbit II: General case
, 2013 Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit ...
Barbara Gentz +9 more
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Periodic orbits, breaktime and localization [PDF]
Journal of Physics A: Mathematical and General, 1998 The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in the field of `Quantum Chaos'.
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Period-Multiplying Bifurcations in the Gravitational Field of Asteroids
AerospacePeriodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids ...
P. Rishi Krishna, Joel George Manathara
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A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems
, 1999 We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system.
B. Eckhardt +21 more
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On the noise-induced passage through an unstable periodic orbit I: Two-level model [PDF]
, 2003 We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit.
Berglund, Nils, Gentz, Barbara
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, 2015 Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical ...
Bedford T +17 more
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Periodic orbits of maps of 𝑌 [PDF]
Transactions of the American Mathematical Society, 1989 We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = { z ∈ C : z 3
Michał Misiurewicz +2 more
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Stabilizing periodic orbits above the elliptic plane in the solar sail 3-body problem [PDF]
, 2008 We consider periodic orbits high above the ecliptic plane in the Elliptic Restricted Three-Body Problem where the third massless body is a solar sail.
Biggs, J.D., McInnes, C., Waters, T.
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, 2010 The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters.
A. Altland +4 more
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