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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 129 (1995), S. 245-304 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For linear scalar parabolic equations such as $$u_t = u_{xx} + a(t,x)u_x + b(t,x)u$$ on a finite interval 0≦x≦π, with various boundary conditions, we obtain canonical Floquet solutions u n (t, x). These solutions are characterized by the property that z(u n (t, x))=n for all tεℝ, where z(·) denotes the zero crossing (lap) number of Matano. The coefficients a(t, x) and b(t, x) are not assumed to be periodic in t, but if they are, the solutions u n (t, x) reduce to the standard Floquet solutions. Our results may naturally be expressed in the language of linear skew product flows. In this context, we obtain for each N≧1 an exponential dichotomy between the bundles span {u n (·,·)} n =1/N and $$\overline {span} \{ u_n ( \cdot , \cdot )\} _{n = N + 1}^\infty $$ .
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 7 (1995), S. 375-407 
    ISSN: 1572-9222
    Keywords: Lorenz type attractors ; conventional Floquet exponents ; hyperbolicity conditions ; saddle-node bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Lorenz type attractors are found from a codimension one bifurcation of a system on the boundary of Morse-Smale systems. Conditions of their emerging are formulated in terms of conventional Floquet exponents of homoclinic orbits—a new characteristic of homoclinic orbits at the bifurcation moment.
    Type of Medium: Electronic Resource
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