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  • 1985-1989  (3)
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Material
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 63-74 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract From a large class of diffeomorphisms in the plane, which are known to produce chaotic dynamics, we explicitly construct their continuous suspension on a three dimensional cylinder. This suspension is smooth (C 1) and can be characterized by the choice of two smooth functions on the unit interval, which have to fulfill certain boundary conditions. For the case of entire Cremona transformations, we are able to construct the corresponding autonomous differential equations of the flow explicitly. Thus it is possible to relate properties of discrete maps to those of ordinary differential equations in a quantitative manner. Furthermore, our construction makes it possible to study the exact solutions of chaotic differential-equations directly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01239015
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Instability in degenerate two-photon running wave laser (1989)
    Springer
    The European physical journal 77 (1989), S. 157-162 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k〉1+r(k=κ/γ⊥,r=γ∥/γ⊥; κ is the cavity loss of the field and γ∥,γ⊥ are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr〈k〈(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313633
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser (1989)
    Springer
    The European physical journal 77 (1989), S. 163-174 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313634
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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