## Structural stability of $$C^1$$ diffeomorphisms.(English)Zbl 0343.58009

### MSC:

 37C75 Stability theory for smooth dynamical systems 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 58C15 Implicit function theorems; global Newton methods on manifolds 37D99 Dynamical systems with hyperbolic behavior
Full Text:

### References:

 [1] Abraham, R; Robbin, J, Transversal mappings and flows, (1967), Benjamin New York · Zbl 0171.44404 [2] Anosov, D, Geodesic flows on closed Riemannian manifolds of negative curvature, (), 1969 [3] {\scC. Camacho and R. Mañé}, Stability theorems for flows on open two dimensional manifolds. [4] de Melo, W, Structural stability of diffeomorphisms on two-manifolds, Invent. math., 21, 233-246, (1973) · Zbl 0291.58011 [5] Dieudonné, J, Foundations of modern analysis, (1960), Academic Press New York · Zbl 0100.04201 [6] Fenichel, N, Persistence and smoothness of invariant manifolds for flows, Indiana univ. math. J., 21, 193-226, (1971) · Zbl 0246.58015 [7] Franks, J, Necessary conditions for stability of diffeomorphisms, Trans. amer. math. soc., 158, 301-308, (1972) · Zbl 0219.58005 [8] {\scJ. Franks}, Notes on manifolds of Cr mappings, to appear. [9] Franks, J, Differentiably ω-stable diffeomorphisms, Topology, 11, 107-113, (1972) · Zbl 0232.58006 [10] Franks, J, Time dependent stable diffeomorphism, Invent. math., 24, 163-172, (1974) · Zbl 0275.58011 [11] Guckenheimer, J, Absolutely ω-stable diffeomorphisms, Topology, 11, 195-197, (1972) · Zbl 0246.58013 [12] Hirsch, M; Pugh, C, Stable manifolds and hyperbolic sets, (), 133-163 [13] {\scM. Hirsch, C. Pugh, and M. Shub}, Invariant manifolds, to appear. [14] Hirsch, M; Palis, J; Pugh, C; Shub, M, Neighborhoods of hyperbolic sets, Invent. math., 9, 121-134, (1970) · Zbl 0191.21701 [15] Irwin, M, On the smoothness of the composition map, Oxford quart. J. math., 23, 113-133, (1972) · Zbl 0235.46067 [16] Mañé, R, Expansive diffeomorphisms, (), 162-174 [17] Moser, J, On a theorem of Anosov, J. differential equations, 5, 411-440, (1969) · Zbl 0169.42303 [18] Nash, J, The embedding problem for Riemannian manifolds, Ann. of math., 63, 20-63, (1956) · Zbl 0070.38603 [19] Newhouse, S, Hyperbolic limit sets, Trans. amer. math. soc., 167, 125-150, (1972) · Zbl 0239.58009 [20] {\scS. Newhouse and J. Palis}, Cycles and bifurcation theory, to appear. · Zbl 0322.58009 [21] Nitecki, Z, Differentiable dynamics, (1971), M.I.T. Press Cambridge, Mass [22] Palis, J, () [23] Palis, J, On Morse-Smale dynamical systems, Topology, 8, 385-405, (1969) · Zbl 0189.23902 [24] Palis, J; Smale, S, Structural stability theorems, (), 223-232 · Zbl 0214.50702 [25] Peixoto, M, Structural stability on two dimensional manifolds, Topology, 1, 101-120, (1962) · Zbl 0107.07103 [26] Pugh, C; Shub, M, The ω-stability theorems for flows, Invent. math., 11, 150-158, (1970) · Zbl 0212.29102 [27] Robbin, J, A structural stability theorem, Ann. of math., 94, 447-493, (1971) · Zbl 0224.58005 [28] Robinson, R.C, Structural stability of vector fields, Ann. of math., 99, 154-175, (1974) · Zbl 0275.58012 [29] Robinson, R.C, Structural stability of C1 flows, (), 262-277 [30] Sacker, R, A perturbation theorem for invariant manifolds and Hölder continuity, J. math. mech., 18, 705-762, (1969) · Zbl 0218.34046 [31] Schwartz, J, Nonlinear functional analysis, (1969), Gordon and Breach New York · Zbl 0203.14501 [32] Smale, S, Differentiable dynamical systems, Bull. amer. math. soc., 73, 747-817, (1967) · Zbl 0202.55202 [33] Shub, M, Stability and genericity for diffeomorphisms, (), 492-514 · Zbl 0289.58013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.