# zbMATH — the first resource for mathematics

##### Examples
 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.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 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)
Expanding Lorenz attractors through resonant double homoclinic loops. (English) Zbl 1093.37022
Summary: We study the existence of Lorenz attractors in the unfolding of resonant double homoclinic loops in dimension three. Our results generalize the ones obtained by {\it C. Robinson} [SIAM J. Math. Anal. 32, 119--141 (2000; Zbl 0978.37013)] in two ways. First, we obtain attractors instead of weak attractors obtained there. Second, we enlarge considerably the region in the parameter space corresponding to flows presenting expanding Lorenz attractors. The proof is based on rescaling techniques of {\it J. Palis} and {\it F. Takens} [Hyperbolicity and sensitive choatic dynamics at homoclinic bifurcations. Fractal dimensions and infinitely many attractors. Cambridge Studies in Advanced Mathematics. 35. Cambridge: Cambridge University Press (1993; Zbl 0790.58014)] to obtain convergence to noncontinuous maps.

##### MSC:
 37G20 Hyperbolic singular points with homoclinic trajectories 37C70 Attractors and repellers, topological structure 37D45 Strange attractors, chaotic dynamics 37D99 Dynamical systems with hyperbolic behavior
Full Text: