scholarly journals Semi-classical quantization rules for a periodic orbit of hyperbolic type

2016 ◽  
Author(s):  
Hanen Louati ◽  
Michel Rouleux
Keyword(s):  
Periodic Orbit ◽  
Hyperbolic Type ◽  
Quantization Rules

QUANTIZATION RULES FOR STRONGLY CHAOTIC SYSTEMS

1992 ◽  
Vol 06 (27) ◽  
pp. 1691-1719 ◽  
Author(s):  
R. AURICH ◽  
J. BOLTE
Keyword(s):  
Periodic Orbit ◽  
Chaotic Systems ◽  
Level Density ◽  
Quantization Condition ◽  
Periodic Orbit Theory ◽  
Symmetry Classes ◽  
Dynamical Zeta Function ◽  
The Mean ◽  
Orbit Theory ◽  
Quantization Rules

We discuss the quantization of strongly chaotic systems and apply several quantization rules to a model system given by the unconstrained motion of a particle on a compact surface of constant negative Gaussian curvature. We study the periodic-orbit theory for distinct symmetry classes corresponding to a parity operation which is always present when such a surface has genus two. Recently, several quantization rules based on periodic orbit theory have been introduced. We compare quantizations using the dynamical zeta function Z(s) with the quantization condition [Formula: see text] where a periodic-orbit expression for the spectral staircase N(E) is used. A general discussion of the efficiency of periodic-orbit quantization then allows us to compare the different methods. The system dependence of the efficiency, which is determined by the topological entropy τ and the mean level density [Formula: see text], is emphasized.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

A new approach to the hydraulic fracture geometric dimensions determination

2017 ◽  
Vol 12 (1) ◽  
pp. 126-134
Author(s):  
A.M. Ilyasov
Keyword(s):  
Exact Solution ◽  
Hydraulic Fracture ◽  
Pressure Gauge ◽  
Hyperbolic Type ◽  
Fluid Injection ◽  
Fracturing Fluid ◽  
New Approach ◽  
Gauge Data ◽  
Bottomhole Pressure ◽  
Half Length

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.

Periodic orbit expansions for the Lorentz gas

1994 ◽  
Vol 75 (3-4) ◽  
pp. 553-584 ◽  
Author(s):  
Gary P. Morris ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas
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