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)
Symmetry breaking and bifurcations in complex Lorenz model. (Ukrainian. English summary) Zbl 1079.37504
Summary: The concept of broken symmetry is used to study stability of equilibrium and time doubly-periodic bifurcating solutions of the complex nonresonant Lorenz model as a function of the frequency detuning on the basis of modified Hopf theory. By contrast to the well-known real Lorenz equations, the system in question is invariant under the action of Lie group transformations (rotations in complex planes) and an invariant set of stationary points is found to bifurcate into an invariant torus, which is stable under the detuning exceeding its critical value. If the detuning then goes downward, numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed in the vicinity of zero detuning.

37D45Strange attractors, chaotic dynamics
34C60Qualitative investigation and simulation of models (ODE)
82C05Classical dynamic and nonequilibrium statistical mechanics (general)
Full Text: Link