Now showing items 1-9 of 9

    • A note on the relationship between spectral radius and norms of bounded linear operators 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2009)
      Article
      Open Access
      Let X be a Banach space and L ( X ) be the Banach algebra of bounded operators on X . In this note we prove that if we have a compact subset K of a commutative sub-algebra of L ( X ), and given " > 0, then ...
    • A result on class-C1 linearization of contractions in infinite dimensions 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2002)
      Article
      Open Access
    • An example on Lyapunov stability and linearization 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2020-01-01)
      Article
      Restricted access - publisher's policy
      The purpose of this paper is to present an example of a (in the Fréchet sense) discrete dynamical system in a infinite-dimensional separable Hilbert space for which the origin is an exponentially asymptotically stable ...
    • An invertible contraction that is not C<sup>1</sup>-linearizable 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2004)
      Article
      Open Access
      We present an example of a smooth invertible contraction in aninfinite-dimensional Hilbert space that is not locally ${\mathcalC}^{1}$-linearizable near its fixed point.
    • Invertible contractions and asymptotically stable ODE´s that are not C<sup>1</sup>-linearizable 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2005)
      Article
      Open Access
      We present an example of a contraction di®eomorphism in in¯nite dimensions that is not C1-linearizable, and we construct a regular ordinary di®erential equation in a Hilbert space whose time-one map is that di®eomorphism. ...
    • Known results and open problems on C1 linearization in Banach spaces 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2012)
      Article
      Open Access
      The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open ...
    • Linearization of class C1 for contractions on Banach Spaces 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2003)
      External research report
      Open Access
      In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant ...
    • Smooth linearization for a saddle on Banach spaces 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2003)
      Article
      Open Access
      As a continuation of a previous work on linearization of class C1 of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions ...
    • Stability problems in nonautonomous linear differential equations in infinite dimensions 

      Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de; Nakassima, G. K. (2020-06-01)
      Article
      Open Access
      In this paper we study the robustness of the stability in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional Banach spaces. Some applications are obtained to ...