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Topological theory of fixed points on infinite-dimensional manifolds

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Global Analysis — Studies and Applications I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1108))

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References

  1. Borisovich, Yu.G. Rotation of Weakly Continuous Vector Fields, Dokl. AN SSSR, 1960, vol. 131, N 2.

    Google Scholar 

  2. Borisovich, Yu.G. Rotation of Weakly Continuous Vector Fields, Trudy Tbil. mat. in-ta im. Razmadze AN GSSR, 1961, vol. 27.

    Google Scholar 

  3. Borisovich, Yu.G. About an Application of the Concept of Rotation of Vector Field, Dokl. AN SSSR, 1963, vol. 153, N 1.

    Google Scholar 

  4. Borisovich, Yu.G. To the Browder Fixed Point Theorem, Trudy seminara po funkts. analizu, Voronezh, 1963, issue 7.

    Google Scholar 

  5. Borisovich, Yu.G. About Perturbation of a Completely Continuous Vector Field by a Weakly Continuous Operator, Trudy seminara po funkts. analizu, Voronezh, 1963, issue 7.

    Google Scholar 

  6. Borisovich, Yu.G. On Bifurcation Points of Positive and Semipositive Operators, In: Functional Analysis and the Theory of Functions, Kazan, 1967, issue 4.

    Google Scholar 

  7. Borisovich, Yu.G. On Relative Rotation of Compact Vector Fields in Linear Spaces, Trudy seminara po funkts. analizu, Voronezh, 1969, issue 12.

    Google Scholar 

  8. Borisovich, Yu.G. Relative Rotation of Compact Vector Fields and the Lefschetz Number, Trudy seminara po funkts. analizu, Voronezh, 1969, issue 12.

    Google Scholar 

  9. Borisovich, Yu.G. Topology and Nonlinear Functional Analysis (Report presented at an International Congress on Topology), Uspehi Mat. Nauk, 1979, vol. 34, N 6.

    Google Scholar 

  10. Borisovich, Yu.G., Bliznyakov, N.M., Izrailevich, Ya.A., and Fomenko, T.N. An Introduction to Topology, Vysshaya shkola, Moscow, 1980.

    MATH  Google Scholar 

  11. Borisovich, Yu.G. and Gliklikh, Yu.E. The Lefschetz Number of Mappings of Banach Manifolds and the Relatedness Theorem, Trudy mat. fac. VGU, Voronezh, 1973, issue 11.

    Google Scholar 

  12. Borisovich, Yu.G. and Gliklikh, Yu.E. On Generation of a New Type of Closed Curves from Periodic Orbit of Vector Field Upon Varying the Metric of Riemannian Manifold, Trudy NIIM, Voronezh State University, Voronezh, 1975, issue 20.

    Google Scholar 

  13. Borisovich, Yu.G. and Gliklikh, Yu.E. On a Class of Closed Curves, Which Appears in the Theory of Vector Fields on Riemannian Manifolds, Deposited in VINITI on January 29, 1978, No. 2164-78.

    Google Scholar 

  14. Borisovič, Ju.G. and Gliklih, Ju.E. Fixed Points of Mappings of Banach Manifolds and some Applications. Nonlinear Analysis: Theory, Methods and Applications, 1980, vol. 4, N 1.

    Google Scholar 

  15. Borisovich, Yu.G. and Sapronov, Yu.I. To the Topological Theory of Compact Contractible Mappings, Trudy seminara po funkts. analizu, Voronezh, 1969, issue 12.

    Google Scholar 

  16. Borisovich, O.Yu. and Khaikin, A.L. On the Concept of Rotation of Vector Field on Manifold, Trudy NIIM VGU, Voronezh, 1975, issue 20.

    Google Scholar 

  17. Browder, F.E. Fixed Point Theorems on Infinite-Dimensional Manifolds, Trans. AMS, 1965, vol. 119, N 2.

    Google Scholar 

  18. Gliklikh, Yu.E. Integral Operators on Manifolds, Trudy mat. fac. VGU, Voronezh, 1971, issue 4.

    Google Scholar 

  19. Gliklikh, Yu.E. About a Generalization of the Hopf-Rinow Theorem on Geodesics, Uspehi Mat. Nauk, 1974, vol. 29, N 6.

    Google Scholar 

  20. Gliklikh, Yu.E. About a Shift Operator Along the Trajectories of Functional Differential Equations on Smooth Manifolds, Trudy NIIM VGU, Voronezh, 1975, issue 17.

    Google Scholar 

  21. Gliklikh, Yu.E. On Pseudo-Integral Curves of Functional Differential Equations on Riemannian Manifolds, In: Methods of Solving Operator Equations, Voronezh, 1978.

    Google Scholar 

  22. Gliklikh, Yu.E. On an Analog of Differential Equations with Discrete Delay on Riemannian Manifolds, Deposited in VINITI on March 20, 1980, No. 1089-80 Dep.

    Google Scholar 

  23. Gliklikh, Yu.E. and Khaikin, A.L. On Periodic Integral Curves of Vector Fields on Lie Groups, In: Applied Analysis, Voronezh, 1979.

    Google Scholar 

  24. Graff, R.A. Elements of Nonlinear Functional Analysis, Memoirs of AMS, 1978, vol. 206.

    Google Scholar 

  25. Zabreiko, P.P., Krasnosel'sky, M.A., and Strygin, V.V. On Invariance Principles of Rotation, Izv. vuzov ser. mat., 1972, vol. 5.

    Google Scholar 

  26. Krasnosel'sky, M.A. Topological Methods in the Theory of Nonlinear Integral Equations, Gostekhizdat, Moscow, 1956.

    Google Scholar 

  27. Krasnosel'sky, M.A. Positive Solutions of Operator Equations, Gostekhizdat, Moscow, 1962.

    Google Scholar 

  28. Krasnosel'sky, M.A. and Zabreiko, P.P. Geometrical Methods of Nonlinear Analysis, Nauka, Moscow, 1975.

    Google Scholar 

  29. Leray, J. Théorie des points fixes: indices total et nomber de Lefschetz, Bull. Soc. Math. France, 1959, vol. 87.

    Google Scholar 

  30. Nagumo, M. Degree of Mapping in Linear Local Convex Topological Spaces, Amer. J. of Math., 1951, vol. 73, N 3.

    Google Scholar 

  31. Penot, J.-P. Weak Topology on Functional Manifolds. Global Analysis and its Applications, Vienna, IAEA, 1974, vol. 3.

    Google Scholar 

  32. Sapronov, Yu.I. To Homotopic Classification of Condensing Mappings, Trudy mat. fac. VGU, Voronezh, 1972, N 6.

    Google Scholar 

  33. Sadovsky, B.N. On Noncompactness Measures and Condensing Operators, In: Problems of Mathematical Analysis of Complex Systems, Voronezh, 1968, issue 2.

    Google Scholar 

  34. Sadovsky, B.N. Limiting Compact and Condensing Operators, Uspehi Mat. Nauk, 1972, vol. 27, N 1.

    Google Scholar 

  35. Spanier, E. Algebraic Topology, New York, 1966.

    Google Scholar 

  36. Fuks, L.B., Fomenko, A.T., and Gutenmakher, V.L. Homotopic Topology, Moscow State University, Moscow, 1969.

    Google Scholar 

  37. Fuller, F.B. The Homotopy Theory of Coincidences, Ann. of Math., 1954, vol. 59, N 2.

    Google Scholar 

  38. Fournier, G. Généralisations du théorème de Lefschetz pour des espases non-compacts, I, II, III.-Bull. Acad. Polon. Sci., Ser. Math. Astron. Phys., 1975, vol. 23, N 6, pp 693–699, 701–706, 707–711.

    MathSciNet  MATH  Google Scholar 

  39. Fenske, C.C. and Peitgen, H.-O. On Fixed Points of Zero Index in Asymptotic Fixed Point Theory, Pacific J. Math., 1976, vol. 66, N 2, pp 391–410.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Voronezh State University, 394693, Voronezh, USSR

    Yu. G. Borisovich & Yu. E. Gliklikh

Authors
  1. Yu. G. Borisovich
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  2. Yu. E. Gliklikh
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Yurii G. Borisovich Yurii E. Gliklikh A. M. Vershik

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© 1984 Springer-Verlag

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Borisovich, Y.G., Gliklikh, Y.E. (1984). Topological theory of fixed points on infinite-dimensional manifolds. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications I. Lecture Notes in Mathematics, vol 1108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099549

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  • DOI: https://doi.org/10.1007/BFb0099549

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  • Print ISBN: 978-3-540-13910-2

  • Online ISBN: 978-3-540-39132-6

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