Saddle connections in parabolic differential equations
DOI:
https://doi.org/10.22199/S07160917.1994.0001.00005Keywords:
Parabolicas, Funciones, Ecuaciones diferenciales parabólicasAbstract
We assume the existence of a saddle connection between two hyperbolic equilibrium points. Necessary and sufficient conditzons are given for the existence of a connection for the perturbed equations. These connections are obtained from the zeros of a finite number of bifurcation functions.
References
[1] C. M. Blázquez, E. Turna Heteroclinic bifurcation in Banach spaces Lectures NoteS in Mathematics 1331(1988),12-38.
[2] C. M. Blázquez Transverse homoclinic orbit in periodically perturbed parabolic equations . Non Linear Analysis 10, No 11J (1986 ),1277-1291.
[3] C. M. Blázquez Bifurcation frorn a homoclinic orbit in parabolic differential equations Proc. Roy. Soc. Edin.103A (1986), 26.5-274.
[4] S . M. Chow, B. Deng Homoclinic and heteroclinic bifurcations in Banach spaces Preprint. Michigan State University
[5] S . M. Chow, J. K. Hale An exarnple of bifurcation to homoclinic orbits of Dif. Eq.37J.(1980).
[6] A. Friedman Hold, Rinehart and Winston 1969. Partial differential equation.
[7] J. K. Hale, X. B. Lin Heteroclinic orbit for retarded functional differential equation LCDS Report 8439 Brown University 1984
[8] .J. K. Hale Introduction to dynamic bifurcation. Lecture Notes in Mathematies. Springer Verlag, 1057 (1984).
[9] D. Henry Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, Springer Verlag, 840 (1981).
[10] X. B. Liu Exponential dichotomies and homoclinic orbit in retarded Functional Differential Equations LCDS Report 8439 Brown University. may 1984.
[11] A. Pazy Semigroups of linear operators and applications to partial differential equations Appl. Math. Se.. 44, Springer Verlag ( 1983)
[12] L. P. Sil'nikov 119 On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Math. USSR Sbornik, Mat. Sbornik Tom 77 vol 6(1968), 119.
[2] C. M. Blázquez Transverse homoclinic orbit in periodically perturbed parabolic equations . Non Linear Analysis 10, No 11J (1986 ),1277-1291.
[3] C. M. Blázquez Bifurcation frorn a homoclinic orbit in parabolic differential equations Proc. Roy. Soc. Edin.103A (1986), 26.5-274.
[4] S . M. Chow, B. Deng Homoclinic and heteroclinic bifurcations in Banach spaces Preprint. Michigan State University
[5] S . M. Chow, J. K. Hale An exarnple of bifurcation to homoclinic orbits of Dif. Eq.37J.(1980).
[6] A. Friedman Hold, Rinehart and Winston 1969. Partial differential equation.
[7] J. K. Hale, X. B. Lin Heteroclinic orbit for retarded functional differential equation LCDS Report 8439 Brown University 1984
[8] .J. K. Hale Introduction to dynamic bifurcation. Lecture Notes in Mathematies. Springer Verlag, 1057 (1984).
[9] D. Henry Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, Springer Verlag, 840 (1981).
[10] X. B. Liu Exponential dichotomies and homoclinic orbit in retarded Functional Differential Equations LCDS Report 8439 Brown University. may 1984.
[11] A. Pazy Semigroups of linear operators and applications to partial differential equations Appl. Math. Se.. 44, Springer Verlag ( 1983)
[12] L. P. Sil'nikov 119 On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Math. USSR Sbornik, Mat. Sbornik Tom 77 vol 6(1968), 119.
Published
2018-04-03
How to Cite
[1]
C. M. Blázquez and E. Tuma, “Saddle connections in parabolic differential equations”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 25-34, Apr. 2018.
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