I'm trying solve the following problem:
Let $M$ be a manifold and $X$ be a complete $C^1$ vector field. Suppose that the foward orbit and backward orbit of every point on $M$ is dense in $M$. Then $M$ is compact.
There is any hint to this problem?.
2026-04-11 12:16:44.1775909804
Vector Field with dense orbits
108 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MANIFOLDS
- a problem related with path lifting property
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- Using the calculus of one forms prove this identity
- "Defining a smooth structure on a topological manifold with boundary"
- On the differentiable manifold definition given by Serge Lang
- Equivalence of different "balls" in Riemannian manifold.
- Hyperboloid is a manifold
- Integration of one-form
- The graph of a smooth map is a manifold
Related Questions in DIFFERENTIAL-TOPOLOGY
- Getting a self-homeomorphism of the cylinder from a self-homeomorphism of the circle
- what is Sierpiński topology?
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- The regularity of intersection of a minimal surface and a surface of positive mean curvature?
- What's the regularity of the level set of a ''semi-nondegenerate" smooth function on closed manifold?
- Help me to prove related path component and open ball
- Poincarè duals in complex projective space and homotopy
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- Prove that the sets in $\mathbb{R}^n$ which are both open and closed are $\emptyset$ and $\mathbb{R}^n$
Related Questions in VECTOR-FIELDS
- Does curl vector influence the final destination of a particle?
- Using the calculus of one forms prove this identity
- In a directional slope field, how can a straight line be a solution to a differential equation?
- Partial Differential Equation using theory of manifolds
- If $\nabla X=h \cdot \text{Id}_{TM}$ for a vector field $X$ and $h \in C^{\infty}(M)$, is $h$ constant?
- Equivalent definition of vector field over $S^2$
- Study of a " flow "
- Extension of a gradient field
- how to sketch the field lines of $F(x,y)=(\sin y,-\sin x)$?
- Is a vector field a mathematical field?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?