Spectral splittings in the Conley index theory

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• 作者：Piotr Bart?omiejczyk
• 关键词：Primary 55T05 ; Secondary 37B30 ; Spectral sequence ; Morse decomposition ; connection matrix
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：17
• 期：2
• 页码：403-412
• 全文大小：490 KB
• 参考文献：1.Bart?omiejczyk P.: The Conley index and spectral sequences. Topol. Methods Nonlinear Anal. 25, 195-03 (2005)MATH MathSciNet
  2.Bart?omiejczyk P.: Connection graphs. Fund. Math. 192, 93-10 (2006)MATH MathSciNet CrossRef
  3.Bart?omiejczyk P.: Simple connection matrices. Ann. Polon. Math. 90, 77-7 (2007)MATH MathSciNet CrossRef
  4.Bart?omiejczyk P.: Spectral sequences and detailed connection matrices. Topol. Methods Nonlinear Anal. 34, 187-00 (2009)MATH MathSciNet
  5.C. Conley, Isolated Invariant Sets and the Morse Index.CBMS Reg. Conf. Ser. Math. 38, Amer. Math. Soc., Providence, RI, 1978.
  6.Conley C., Zehnder E.: Morse-type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure Appl. Math. 37, 207-53 (1984)MATH MathSciNet CrossRef
  7.Cornea O., de Rezende K.A., Silveira M.R.: Spectral sequences in Conley’s theory. Ergodic Theory Dynam. Systems 30, 1009-054 (2010)MATH MathSciNet CrossRef
  8.Fiedler B., Mischaikow K.: Dynamics of bifurcations for variational problems with O(3) equivariance: A Conley index approach. Arch. Ration. Mech. Anal. 119, 145-96 (1992)MATH MathSciNet CrossRef
  9.Franzosa R.: The connection matrix theory for Morse decompositions. Trans. Amer. Math. Soc. 311, 561-92 (1989)MATH MathSciNet CrossRef
  10.K. Mischaikow and M. Mrozek, The Conley index theory. In: Handbook of Dynamical Systems II: Towards Applications, Elsevier, Singapore, 2002, 393-60.
  11.Razvan M.R.: On Conley’s fundamental theorem of dynamical systems.Int.J. Math. Math. Sci. 2004, 1397-401 (2004)MATH MathSciNet
  12.Reineck J.: TheconnectionmatrixinMorse-Smale flows. Trans. Amer. Math. Soc. 322, 523-45 (1990)MATH MathSciNet CrossRef
  13.Robbin J.W., Salamon D.: Lyapunov maps, simplicial complexes and the Stone functor. Ergodic Theory Dynam. Systems 12, 153-83 (1992)MATH MathSciNet CrossRef
  14.Salamon D.: Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc. 291, 1-1 (1985)MATH MathSciNet CrossRef
  15.Zeeman E.C.: On the filtered differential group. Ann. of Math. 66(2), 557-85 (1957)MATH MathSciNet CrossRef
  
• 作者单位：Piotr Bart?omiejczyk (1)
  
  1. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

We introduce spectral splittings and spectral graphs. We explain the relation between spectral splittings, graphs and sequences. Mathematics Subject Classification Primary 55T05 Secondary 37B30