zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Geometric singular perturbation theory. (English) Zbl 0840.58040
Johnson, Russell (ed.), Dynamical systems. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Montecatini Terme, Italy, June 13-22, 1994. Berlin: Springer-Verlag. Lect. Notes Math. 1609, 44-118 (1995).
These are lectures given at the second session of the Centro Internazionale Matematico Estivo (CIME) in 1994. The goal is an exposition of the geometric approach to singular perturbation problems. Singularly perturbed equations gain their special structure from the presence of differing time scales. The fundamental tool in their analysis, from perspective taken in the lectures, is the set of theorems due to Fenichel. The first step is then to explain these theorems and their significance. At the same time, new proofs of Fenichel’s three main results are outlined. The contents of the lectures: introduction, invariant manifold theorems, Fenichel normal form, tracking with differential forms, exchange lemma, generalizations and future directions [58 ref.]. For the entire collection see [Zbl 0822.00008].

37J40Perturbations, normal forms, small divisors, KAM theory, Arnol’d diffusion
37-01Instructional exposition (dynamical systems and ergodic theory)
37-99Dynamic systems and ergodic theory (MSC2000)