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Regularity of extremal solutions of semilinear elliptic problems with non-convex nonlinearities on general domains
Topological stability from Gromov-Hausdorff viewpoint
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil |
We combine the classical Gromov-Hausdorff metric [
References:
[1] |
N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Recent advances. North-Holland Mathematical Library, 52. North-Holland Publishing Co. , Amsterdam, 1994. |
[2] |
D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, 33. American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/033. |
[3] |
R. M. Dudley,
On sequential convergence, Trans. Amer. Math. Soc., 112 (1964), 483-507.
doi: 10.1090/S0002-9947-1964-0175081-6. |
[4] |
A. Edrei,
On mappings which do not increase small distances, Proc. London Math. Soc., 2 (1952), 272-278.
doi: 10.1112/plms/s3-2.1.272. |
[5] |
M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Based on the 1981 French original. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates. Progress in Mathematics, 152. Birkhäuser Boston, Inc. , Boston, MA, 1999. |
[6] |
R. Metzger, C.A. Morales and Ph. Thieullen,
Topological stability in set-valued dynamics, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 1965-1975.
doi: 10.3934/dcdsb.2017115. |
[7] |
Z. Nitecki,
On semi-stability for diffeomorphisms, Invent. Math., 14 (1971), 83-122.
doi: 10.1007/BF01405359. |
[8] |
Z. Nitecki, Differentiable Dynamics. An Introduction to the Orbit Structure of Diffeomorphisms, The Press M.I.T., Cambridge, Mass.-London, 1971.
![]() ![]() |
[9] |
B. Pepo,
Fixed points for contractive mappings of third order in pseudo-quasimetric spaces, Indag. Math. (N.S.), 1 (1990), 473-481.
doi: 10.1016/0019-3577(90)90015-F. |
[10] |
P. Petersen, Riemannian Geometry. Third Edition, Graduate Texts in Mathematics, 171. Springer, Cham, 2016.
doi: 10.1007/978-3-319-26654-1. |
[11] |
P. Walters, On the pseudo-orbit tracing property and its relationship to stability, The structure of attractors in dynamical systems (Proc. Conf. , North Dakota State Univ. , Fargo, N. D. , 1977), Lecture Notes in Math. , Springer, Berlin, 668 (1978), 231-244. |
[12] |
P. Walters,
Anosov diffeomorphisms are topologically stable, Topology, 9 (1970), 71-78.
doi: 10.1016/0040-9383(70)90051-0. |
[13] |
K. Yano,
Topologically stable homeomorphisms of the circle, Nagoya Math. J., 79 (1980), 145-149.
doi: 10.1017/S0027763000018997. |
show all references
References:
[1] |
N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Recent advances. North-Holland Mathematical Library, 52. North-Holland Publishing Co. , Amsterdam, 1994. |
[2] |
D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, 33. American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/033. |
[3] |
R. M. Dudley,
On sequential convergence, Trans. Amer. Math. Soc., 112 (1964), 483-507.
doi: 10.1090/S0002-9947-1964-0175081-6. |
[4] |
A. Edrei,
On mappings which do not increase small distances, Proc. London Math. Soc., 2 (1952), 272-278.
doi: 10.1112/plms/s3-2.1.272. |
[5] |
M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Based on the 1981 French original. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates. Progress in Mathematics, 152. Birkhäuser Boston, Inc. , Boston, MA, 1999. |
[6] |
R. Metzger, C.A. Morales and Ph. Thieullen,
Topological stability in set-valued dynamics, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 1965-1975.
doi: 10.3934/dcdsb.2017115. |
[7] |
Z. Nitecki,
On semi-stability for diffeomorphisms, Invent. Math., 14 (1971), 83-122.
doi: 10.1007/BF01405359. |
[8] |
Z. Nitecki, Differentiable Dynamics. An Introduction to the Orbit Structure of Diffeomorphisms, The Press M.I.T., Cambridge, Mass.-London, 1971.
![]() ![]() |
[9] |
B. Pepo,
Fixed points for contractive mappings of third order in pseudo-quasimetric spaces, Indag. Math. (N.S.), 1 (1990), 473-481.
doi: 10.1016/0019-3577(90)90015-F. |
[10] |
P. Petersen, Riemannian Geometry. Third Edition, Graduate Texts in Mathematics, 171. Springer, Cham, 2016.
doi: 10.1007/978-3-319-26654-1. |
[11] |
P. Walters, On the pseudo-orbit tracing property and its relationship to stability, The structure of attractors in dynamical systems (Proc. Conf. , North Dakota State Univ. , Fargo, N. D. , 1977), Lecture Notes in Math. , Springer, Berlin, 668 (1978), 231-244. |
[12] |
P. Walters,
Anosov diffeomorphisms are topologically stable, Topology, 9 (1970), 71-78.
doi: 10.1016/0040-9383(70)90051-0. |
[13] |
K. Yano,
Topologically stable homeomorphisms of the circle, Nagoya Math. J., 79 (1980), 145-149.
doi: 10.1017/S0027763000018997. |


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