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  • 1
    Electronic Resource
    Electronic Resource
    Local controllability and semigroups of diffeomorphisms (1993)
    Springer
    Acta applicandae mathematicae 32 (1993), S. 1-57 
    Details
    ISSN: 1572-9036
    Keywords: 93BXX ; Local controllability ; vector field ; flow ; Lie bracket
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The local structure of orbits of semigroups, generated by families of diffeomorphisms, is studied by Lie theory methods. New sufficient conditions for local controllability are obtained which take into account ordinary, as well as fast-switching variations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00992082
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  • 2
    Electronic Resource
    Electronic Resource
    Chronological algebras and nonstationary vector fields (1981)
    Springer
    Journal of mathematical sciences 17 (1981), S. 1650-1675 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A calculus is developed, reflecting the most general group-theoretic properties of flows, defined by nonstationary differential equations on manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01084595
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  • 3
    Electronic Resource
    Electronic Resource
    Chronological series and the Cauchy-Kowalevski theorem (1983)
    Springer
    Journal of mathematical sciences 21 (1983), S. 231-250 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the Cauchy problem for a system of partial differential equations. We prove an existence theorem for a solution of this problem which is analytic in the spatial variable under the assumption of measurability and local integrability of the right side with respect to time only. The solution is represented in the form of a chronological series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01084777
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  • 4
    Electronic Resource
    Electronic Resource
    Volterra series and permutation groups (1994)
    Springer
    Journal of mathematical sciences 71 (1994), S. 2409-2433 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Algebraic structures, connected with the asymptotic expansions of perturbations of smooth dynamical systems, are investigated; first of all, the so-called shuffle multiplication for permutations and for iterated integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111557
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  • 5
    Electronic Resource
    Electronic Resource
    On superpositions of continuous functions (1974)
    Springer
    Mathematical notes 16 (1974), S. 897-900 
    Details
    ISSN: 1573-8876
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that if Φ is an arbitrary countable set of continuous functions of n variables, then there exists a continuous, and even infinitely smooth, function ψ(x1,...,xn) such that ψ(x 1, ...,x n ) ≢g [ϕ (f 1(x 1, ... ,f f (x n ))] for any function ϕ from Φ and arbitrary continuous functions g and fi, depending on a single variable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01104251
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  • 6
    Electronic Resource
    Electronic Resource
    Differential-geometric and group-theoretical methods in optimal control theory (1985)
    Springer
    Journal of mathematical sciences 28 (1985), S. 145-182 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Problems arising in the geometry of attainable sets of nonlinear control systems are considered. Old and new results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02105209
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  • 7
    Electronic Resource
    Electronic Resource
    Topology of quadratic maps and hessians of smooth maps (1990)
    Springer
    Journal of mathematical sciences 49 (1990), S. 990-1013 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we study sets of real solutions of systems of quadratic equations and inequalities. The results are used for the local study of more general systems of smooth equations and inequalities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02133177
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  • 8
    Electronic Resource
    Electronic Resource
    Exponential mappings for contact sub-Riemannian structures (1996)
    Springer
    Journal of dynamical and control systems 2 (1996), S. 321-358 
    Details
    ISSN: 1573-8698
    Keywords: 53B ; 49L05 ; Sub-Riemannian geometry ; contact structure ; differential invariants ; conjugate locus ; dut locus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract On sub-Riemannian manifolds any neighborhood of any point contains geodesics which are not length minimizers; the closures of the cut and the conjugate loci of any pointq containq. We study this phenomenon in the case of a contact distribution, essentially in the lowest possible dimension 3, where we extract differential invariants related to the singularities of the cut and the conjugate loci nearq and give a generic classification of these singularities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02269423
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  • 9
    Electronic Resource
    Electronic Resource
    On Morse Theory for Piecewise Smooth Functions (1997)
    Springer
    Journal of dynamical and control systems 3 (1997), S. 449-469 
    Details
    ISSN: 1573-8698
    Keywords: Continuous selection ; critical point ; nonsmooth Morse theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Lower level sets of continuous selections of C 2-functions defined on a smooth manifold in the vicinity of a nondegenerate critical point in the sense of [11] are studied. It is shown that the lower level set is homotopy equivalent to the join of the lower level sets of the smooth and the nonsmooth part, respectively, of the corresponding normal form. Some generalized Morse inequalities are deduced from this result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021810206861
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  • 10
    Electronic Resource
    Electronic Resource
    On morse theory for piecewise smooth functions (1997)
    Springer
    Journal of dynamical and control systems 3 (1997), S. 449-469 
    Details
    ISSN: 1573-8698
    Keywords: 26A27 ; 58C27 ; 90C30 ; Continuous selection ; critical point ; nonsmooth Morse theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Lower level sets of continuous selections ofC 2-functions defined on a smooth manifold in the vicinity of a nondegenerate critical point in the sense of [11] are studied. It is shown that the lower level set is homotopy equivalent to the join of the lower level sets of the smooth and the nonsmooth part, respectively, of the corresponding normal form. Some generalized Morse inequalities are deduced from this result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463278
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