Hilbert’s sixteenth problem

E761264

Hilbert problem

Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.

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Observed surface forms (2)

Surface form	Occurrences
Hilbert’s sixteenth problem (first part)	0
Hilbert’s sixteenth problem (second part)	0

Statements (44)

Predicate	Object
instanceOf	Hilbert problem ⓘ
appearsIn	“Mathematische Probleme” (Hilbert’s 1900 address) NERFINISHED ⓘ
asks	whether there is a uniform upper bound on the number of limit cycles of a polynomial vector field of given degree ⓘ which configurations of ovals can occur for real plane algebraic curves of degree n ⓘ
concerns	arrangement of algebraic curves ⓘ arrangement of algebraic surfaces ⓘ limit cycles of polynomial vector fields on the plane ⓘ number of ovals of real algebraic curves ⓘ position of ovals of real algebraic curves ⓘ possible arrangements of components of real algebraic curves of given degree ⓘ qualitative theory of real polynomial differential equations ⓘ relative position of ovals of real plane algebraic curves ⓘ topology of algebraic curves ⓘ topology of algebraic surfaces ⓘ
degreeOfCurvesMentioned	plane algebraic curves of degree n ⓘ
field	algebraic geometry ⓘ differential equations ⓘ topology ⓘ
hasHilbertProblemNumber	XVI NERFINISHED ⓘ
hasKeyword	limit cycles ⓘ ovals ⓘ polynomial vector fields ⓘ qualitative behavior of solutions ⓘ real algebraic curves ⓘ
hasPart	Hilbert’s sixteenth problem (first part) NERFINISHED ⓘ Hilbert’s sixteenth problem (second part) NERFINISHED ⓘ
influenced	qualitative theory of dynamical systems ⓘ real algebraic geometry NERFINISHED ⓘ topology of real plane curves ⓘ
languageOfOriginalStatement	German ⓘ
namedAfter	David Hilbert NERFINISHED ⓘ
numberInList	16 ⓘ
partOf	Hilbert’s list of 23 problems NERFINISHED ⓘ
posedBy	David Hilbert NERFINISHED ⓘ
presentedAt	International Congress of Mathematicians in Paris NERFINISHED ⓘ
relatedTo	Gudkov’s conjecture NERFINISHED ⓘ Harnack’s inequality NERFINISHED ⓘ Hilbert’s problems NERFINISHED ⓘ Hilbert’s sixteenth problem on limit cycles NERFINISHED ⓘ Rokhlin’s complex orientation formula NERFINISHED ⓘ
statedIn	1900 ⓘ
status	open ⓘ partially solved ⓘ unsolved in full generality ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hilbert’s seventeenth problem → relatedTo → Hilbert’s sixteenth problem ⓘ